If it’s Islam, then no. However, there are other cases where you should say “shoot me”. There’s a rule in Judaism that says, generally, you’re allowed to break a commandment if you think it’ll save your life or the life of another person. However, there are a few commandments you’re not allowed to break, even in that circumstance, and idolatry is one of them. If somebody says, “You have to worship this idol or I’ll kill you”, the right thing would be to let yourself be killed. However, in the case of Islam, which isn’t an idolatrous religion (Jews believe that Muslims worship the same God that Jews do, and idols are a no-no in Islam too), you’re allowed to pretend to convert in order to live. It’s a little trickier if the gunmen wanted you to convert to Christianity, because there’s always been a debate within Judaism if Christianity is considered idolatry or not.
However, that being said, there’s another factor, known as “sanctification of the Name”, which says, among other things, that, if people are trying to exterminate Judaism, you have to fight against them. So, even though, for example, you’re allowed to eat non-kosher food to save your life, if somebody is trying to force you to eat non-kosher food to try to wipe out the religion, you’re not allowed to eat it.