I believe that Jews are not permitted to convert to another religion. While virtually every law in the Torah can be violated to save a life, I don't think that worshipping an idol or a false "diety" is allowed. THAT is what martydom is about, not being a splodeydope and murdering a bunch of innocent women and children as you commit suicide.
Of course, the Islamofascists would likely not give any Jew such a choice, as they seem to so relish the idea of sawing off the heads of living Jews, preferably slowly and in front of a camera.
As I am no authority on Jewish law, I welcome any corrections.
A conversion to islam is the saying of the bismallah..."there is no god but (the islamic)allah..."
I would probably wail like a baby when they put the rusty kitchen knife to my neck...but I sure hope I wouldn't deny my Lord.