My general impression is that they seem to be very fiscally conservative and hawkish re:Israel.
This. I think Mark Levin and Michael Savage fit the bill quite well for *strongly conservative* secular Jewish Republicans, in contrast to someone like Ben Shapiro or Dennis Prager for more religious Jewish Republicans. I think someone who is Bloombergesque describes many of the more moderate secular Jewish Republicans, but they were very anti-Trump and probably don't even ID as Republicans overall.
Michael Bloomberg is a Democrat though? He was a lifelong Democrat before running for mayor. He only ran as a Republican in 2001 because there was no way he could've beaten Mark Green in the Democratic primaries. IIRC, he was originally planning to run for mayor as a Democrat, but Mark Green already had the Democratic nomination sealed up, so he had no choice but to run as a Republican. He's very liberal politically speaking. He sides with Hillary Clinton on virtually every single issue except for stop-and-frisk.