I've seen the tag judeo-christian a few times, and imo that one strikes a better balance between familiarity and accuracy/comprehensiveness.
I'm also under the impression that the gap between Judeo-Christian and Islamic myths is significantly larger than that between Judaist and Christian myths, so we don't really need to put all three under a single tag all the time (maybe only when the question explicitly covers all three?), but I could be wrong about that.
Incidentally, I think it makes sense to have a Bible tag in addition to judeo-christian. You could ask questions about Judeo-Christian myths that aren't in the Bible at all, or are only in the apocrypha, or only in the "canonical" bible. And some people will definitely be more knowledgeable about some of those categories than others (eg, what little I know is all from the canonical Bible). I would be skeptical about tags for individual books and characters in the Bible, but the Bible itself seems pretty useful.