He who disbelieves in Allah after his belief in Him, (is the liar) except he who is compelled while his heart remains steadfast with the faith (has nothing worry). But who opens his breast for infidelity; on these is wrath of Allah, and for them is a great torment.
--Qur’an, Surah 16 (an‑Nahl), verse 100
This verse of the Qur’an refers to the incident when 'Ammar bin Yasir (May Allah be pleased with both) had to utter some words against Islam to save himself from the Quraishite infidels.
The Qur'an clearly allows hiding one 's true faith when one is in danger of one's life. This rule is called taqiyah.
Question 1: What is the meaning of "Taqiyah"?
Answer: Its literal meaning is to safeguard; to defend; to fear; piety (because it saves one from the displeasure of Allah).
Question 2: What is its significance in Islamic terminology?
Answer: In Islamic terminology it means "to save life, honour. or property (either one's own or of other believers) by hiding one's belief or religion".
I imagine the same rule would apply for a Muslim who hides his jihad sympathies.
Al-Taqiyah grants Muslims the Shar'iyee right (legitimacy) to infiltrate the Dar el-Harb (war zone), infiltrate the enemy's cities and forums and plant the seeds of discord and sedition. These agents were acting on behalf of the Muslim authority at war, and therefore were not considered as lying against or denouncing the tenants of Islam.
They were "legitimate" mujahedeen, whose mission was to undermine the enemy's resistance and level of mobilization. One of their major objectives was to cause a split among the enemy's camp while downplaying the issues related to Islam ("Oh, I am not religious." "Oh, that is not Islam, you are mistaken, there is so much misinformation." "Oh, it is in the interpretation." "Brother, Islam is all about peace and love and music just like in the 60s.") In many instances, they convinced their targeted audiences that Jihad is not aimed at them, that indigenous people are not targeted. Meanwhile the (allegedly) "un Islamic" Muslims continued their attacks on the target's property and life (e.g. Lashkar-e Toyiba, Mujahideen and Osama Bin Laden's declaration of war against innocent American civilians).