If it’s heritage too, then there are many who are descendants of Judah who do not realize it. But that does not dictate political beliefs either, of course; and I agree that antisemites do not care either way.
There certainly could be many who don’t realize it. For the time being, they are safer from the islamists. But I don’t expect that to last because basically, there is nobody that is not within their sights. Look even at the Sunni/Shiite issues.
When there are no infidels around, they eat each other alive.
But as far as being Jewish, the issue is those who know it or, actually, what others think you are.
Last names can also give it away, or lead others to suspect. There are some names commonly associated with Jewish heritage.