If people believed in pyramid power, that putting razor blades in pyramids can make them sharper (some people do believe this), and that belief was mocked, ... would anybody complain?
If I mocked the fact that Scientologists believe the Galactic overlord Xenu placed us Thetans inside the bodies of beings in a volcano using interplanetary 747s ... it sounds silly, doesn't it? ... would anybody complain?
If I told you New Agers believe putting crystals on your body can heal you ... and then started mocking that ... probably nobody would say anything.
So what I typically find is people are OK with mocking non-religious beliefs, and the beliefs of other religions, but not their own.
Anyway, I don't think mocking or ridiculous Jewish religious belief is anti-Semitism. I personally think anyone who literally believes Noah took two of every animal on Earth and put it on a boat to be a fool. If that offends some of my fellow Jews, well, so be it. It's nonsense, at least if taken literally. Plus, it's probably borrowed from Sumerian, Babylonian, and Akkadian flood stories which are older.
The Torah was not given to Moses on Mt. Sinai. I think that's ridiculous.
Anti-Semitism and Islamophobia are real phenomena, but I don't think mocking Jewish or Islamic religious belief qualifies or is, per se, a form of bigotry. Now - as for anti-Semitism, no, I don't think all criticism of Israel or its government is anti-Semitic, but I think it can be. David Duke often criticizes Israel, and shows some obvious crossing of that line. Some forms of criticism of Israel replicate the ancient blood libel myth about Jews -- that IS anti-Semitic. And yes, Arabs can be anti-Semites, given the particular meanings of how the word originated in 19th century Germany (even though technically, they are Semites as well.)
BTW, there are places where Christians are persecuted and in some cases even killed for their beliefs, but it's not here in America. One area where I disagree with Trump is that somehow Christian refugees from the Middle East are more "entitled" to refugee status than other persecuted groups, though. (Like, say, the Yezidi.)
Anyone who knows some garden variety white Evangelicals should try this little experiment.
Mention the word "Islam" or "Muslim" to a typical 81%er white Evangelical bigot, then set the timer. My money says 10 seconds won't pass without mockery and/or direct insult of that religion.