Taqya: it's not lying; it's not telling the truth.

[Carnyx]

Taqya: Taqya is not equal to telling lie. Taqya means to hide your real belief for the sake of your safety. Some times, to keep oneself from a danger, one might tell a lie to hide one's real belief, although one is not really a sort of person that uses to tell lies. Ammar for instance (according to some historical records) under the pressure of the sever torture by Kuffar, found no way but denying the prophet hood of the prophet only to the extent of a declaration, but not from the heart. He only did that to get rid of the severe torture and the records say that the prophet assured him that he had not committed sin by that. During the regime of Umawies and Abbasies, many individuals were tortured and murdered merely based on their belief. Many of those ascribed to Shia belief were among them. They therefore needed to practice Taqyah to remain safe. Of course many people might prefer to die for their belief, but it is solely upon the individuals to decide which is more beneficial for the cause.
Muhammad Husayn Ale Kashef Alqeta (one of the famous classic Imami Shia scholars) in his book Asl Ashia Wa Osooleha (pages 314-5) says (translated and summarised by me):

There are three (different) duties about Taqya:
Some times it is obligatory. This is when not doing Taqya causes waste of life (dead) with no benefit.
Some times it is permissible. This is when acting according to the belief without Taqya could result in strengthening the truth. In this case one might reveal the truth or one might observe Taqya.
Some times it is forbidden. This is when Taqya will result in spreading falsehood and misguiding people and restoring oppression.

I think you will agree that the above may sound reasonable to many Muslims and that in fact the practice of many Muslims (and in fact human being) is nothing but the above. In fact Shia uses some of the verses of Quran to prove the permissibility of Taqyah (hiding the real belief) when our safety is in danger and there is no benefit to get in trouble (dying, prison, torture etc.).
At present, of course, safety is not an issue for Shia in most of the Muslim communities. However you might find that occasionally some Shia still practices Taqyah to some extent. This could have different reasons and I agree that the reasons are not always good ones from the point of view of a main stream Muslim. Still, however, you can see that the issue has nothing to do with being Muslim or not.

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TAQIYA Taqiya, or not showing their faith openly by means of pretense, dissimulation, or concealment, is a special type of LYING which is taught and used by Shi\'a Muslims, cf. Sunni Muslims and taqiya. "Taqiya" (or taqiyyah) is related to the terms "taqwa'" and "taqi'" - all have the root meaning of "guarding" something, in this case, the Islamic faith.
This practice, along with the practice of Kithman, or concealing their faith from non-Shi'as, were, and are many places today, a method of self-preservation for the Shi'a community. Historically, the Shiites have been in the minority and have been persecuted by Sunni Muslims who considered them heretics. Shi'as are often persecuted today in Pakistan and Afghanistan and Sunni-Shi'a violence is fairly common. Sunnis would often attempt to force Shi'as to curse the House of Ali - believing that no devout Shiite could commit such an act. As a result of this persecution, the idea of Taqiya emerged. In other words, if a Shi'a Muslim's life is in danger, he may lie as long as he holds true to Ali in his heart.
Shi'as believe that the origin of this line of defence comes from the Qur'an. When Moses returned from the mountain and saw his people worshiping the golden calf, he was understandably angry and asked his brother Aaron why he allowed such a terrible sin to be committed. The Qur'an tells us

When Moses came back to his people, angry and grieved, he said: "Evil it is that ye have done in my place in my absence: did ye make haste to bring on the judgment of your Lord?" He put down the tablets, seized his brother by (the hair of) his head, and dragged him to him. Aaron said: "Son of my mother! the people did indeed reckon me as naught, and went near to slaying me! Make not the enemies rejoice over my misfortune, nor count thou me amongst the people of sin." Moses prayed: "O my Lord! forgive me and my brother! admit us to Thy mercy! for Thou art the Most Merciful of those who show mercy!" Sura 7:150-151 This verse is important because, since all Muslims believe that Aaron is a Prophet, none would criticize him for cowardice.
A more specific justification for Taqiya by the Shi'as is the instance when 'Ammar ibn al-Yasir (one of the companions loyal to 'Ali and considered to be one of the first Shi'a) was detained and tortured by infidels. He renounced his faith in order to escape and immediately went to Muhammad and repented. 'Umar suggested that he be put to death for apostasy, however, Muhammad said that it was better for him to renounce his faith with his lips (while still believing in his heart) than to be burned to death by the infidels.
This account is surprising considering how much emphasis the Qur'an places on martyrdom. Today, many Sunnis criticize 'Ammar for his actions and there is a significant difference of philosophy between Sunnis and Shi`a which creates this dilemma. The Sunnis believe that human beings have little or no free will, while the Shi`a believe that humans enjoy a great deal of free will.
To a Sunni, God decides how, and when, one is going to die and what is going to happen to all people - both believers and unbelievers. Therefore, it makes little difference what decisions one makes - everything is in God's hands, and it is not right to outwardly deny the faith in order to escape torture or death.
By contrast, the Shi'a believe that life is a gift from God and like any gift from God, should be preserved and not squandered. Anything that one can do to save one's life should be done, even if it is contrary to God's laws. In a life-threatening emergency, self-preservation, and the preservation of the faith take precedence over obedience to the shari'ah - in fact, this kind of preservation in such situations would be considered obedience to the shari'ah.
Taqiya is to be practiced only when one fears for one's life, the lives of one's family members, or for the preservation of the faith. In those situations, according to most Shi`a jurisprudents, Taqiya is required!
Some Shiite Traditions promoting Taqiya are

Imam Jafar Sadi (R) said: "Associate your opponents only outwardly and oppose them inwardly." (Ft. #1, Usool al Kafi, p.244) Zararah narrates that I asked a certain question to Imam Baqar (R). He gave me its answer. Another person then asked the same question and the Imam gave him a different answer. Later a third person asked the same question, but the Imam's answer this time was different from the previous two answers. I then asked him: "O, the son of the Messenger (S)! The two persons who just came here to ask you questions were from Iraq and were Shias, yet you gave them contradictory answers". The Imam then answered: "O Zararah! This is good for me as well as for you and this will help us survive and prosper". (Ft. #2 Ibid, p.37)
For more information on this topic, please read this article and this linked section of Relation of Shi\'a Theology to the Qur\'an.
Shia Encyclopedia entry: Taqiyya

Sunni Muslims and taqiya
However, although taqiya is usually seen as a Shia doctrine only, it is practiced and taught also by Sunni Muslims, cf. the discussion of friendship with unbelievers in the entry on FRIENDS. Here just one quotation from a Sunni website, Islam Q&A (موقع الإسلام سؤال وجواب), advising in regard to making friends with non-Muslims:

"Let not the believers take the disbelievers as Awliyaa' (supporters, helpers) instead of the believers, and whoever does that, will never be helped by Allaah in any way, except if you indeed fear a danger from them" [Aal 'Imraan 3:28]
This verse explains all the verses quoted above which forbid taking the kaafirs as friends in general terms. What that refers to is in cases where one has a choice, but in cases of fear and TAQIYAH it is permissible to make friends with them, as much as is essential to protect oneself against their evil. That is subject to the condition that one's faith should not be affected by that friendship and the one who is behaves in that manner out of necessity is not one who behaves in that manner out of choice.
Shaykh Muhammad al-Saalih al-'Uthaymeen (may Allaah have mercy on him) was asked about the ruling on mixing with the kuffaar and treating them kindly hoping that they will become Muslim. He replied:
Undoubtedly the Muslim is obliged to HATE the enemies of Allaah and to disavow them, because this is the way of the Messengers and their followers...
Based on this, it is not permissible for a Muslim to feel any love in his heart towards the enemies of Allaah who are in fact his enemies too...
But if a Muslim treats them with KINDNESS and gentleness in the hope that they will become Muslim and will believe, there is nothing wrong with that, because it comes under the heading of opening their hearts to Islam. But if he despairs of them becoming Muslim, then he should treat them accordingly. This is something that is discussed in detail by the scholars, especially in the book Ahkaam Ahl al-Dhimmah by Ibn al-Qayyim ... (Question #59879: What is meant by taking the kuffaar as friends? Ruling on mixing with the kuffaar; bold and capital emphasis ours)

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KITHMAN KITHMAN, is the command for Shi\'a Muslims to conceal their religious beliefs from non-Shia's. Kithman is a special variety of Lying .
This practice, along with the practice of Taqiya, were, and are many places today, a method of self-preservation for the Shi'a community. Historically, the Shiites have been in the minority and have been persecuted by Sunni Muslims who considered them heretics.
Traditions from the sixth Shia Imam firmly established this practice:
Imam Jafar Sadiq (R) said:

"One, who exposes something from our religion is like one who intentionally kills us." (Ft. #1 Usool al Kafi, p.88) "You belong to a religion that whosoever conceals it, Allah will honour him and whosoever reveals it, Allah will disgrace him." (Ft. #2, Ibid, p.522).
For more information on this topic, please read this article.

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[Marcus Marulus]

The Polish writer Czeslaw Milosz also wrote about the so-called ketman or kithman:

Even with that, embracing the new faith was not without its problems, as Milosz‘s analysis of the “Ketman” mentality shows. Many retained their old habits. The term Ketman was borrowed from Gobineau’s book, Religions et Philosophies dans l’Asie Centrale (Religions and Philosophies in Central Asia). A Ketman is a person characterized by an external professesion of belief in a dominant New Faith, while internally assenting to different beliefs (CM 79-84). Milosz’s analysis of the varieties of communist Ketman is not as directly theological as some other parts of the book. This is only natural since The Captive Mind assumes, as was shown earlier in this paper, that all the problems it describes--including the phenomenon of Ketman--presuppose a civilization-wide meltdown of the religious imagination, and hence all our problems are theological to the core. Part of what makes this situation a crisis is that it is not, for the most part, consciously recognized as a crisis. However, “the Metaphysical Ketman,” according to Milosz, is not spared this blissful ignorance. He consciously supports the new regime because “the man beholden to this variety of Ketman considers the epoch in which he lives to be anti-metaphysical, hence, one in which metaphysical faith cannot appear” (99). Toward the end of the Ketman chapter Milosz asks whether all the different Ketman poses are a hidden form of pride. He also hints at a possible “act of faith” that could circumvent the need for Ketman (110).

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