Answer based on reading various modern historians that discuss this rather than being a historian!

There are often arguments about terminology, anti-semitism vs anti-Judaism etc. Where Rome acted against the Jews it's in a radically different context to anti-semitism as we think of it and it's not clear how helpful it is to lump them in together. For one thing, in modern times the existence of a largely Jewish state has re-emerged after anti-semitism has been well established in the context of Jews being seen as 'outsiders' etc. whereas at least until Hadrian there was a Jewish state, so acts against that state might blur with acts against Jews.

I think it's also important to remember Rome isn't a monolith. Hadrian for instance came down very hard on Judea, and this may have been to do with his explicitly Hellenistic views (then again, it may simply be a question of Jews being more likely to rebel and Romans having very uncompromising responses to rebellion).

On that note: the strong self-identity of Jews as a people (combined with religious law that made it harder for that to blur) plus messianism and tradition of priests with political power may well have meant there were more likely to be rebellions, and that the rebellions that did occur would be more determined as you see both under Rome and other rulers (e.g. Maccabees under Seleucids).

I'm not aware of any huge antisemitic 'tropes'/stereotypes that seem to have been very influential in the Roman Empire, though obviously in this period people happily talked about 'X people are like Y' so I'm sure there are some negative statements about Jews out there!

In terms of identifying if there was a specific issue with the religion, it's worth comparing with Christians. The latter were usually seen as worse than Jews (until they started to dominate), for various reasons including their lack of comparable pedigree and their evangelism. But in a society where religion is based around common rituals, people refusing to follow those rituals can cause conflict without you actually caring about their own views. Similarly, the sort of commitment on matters of principle that Judaism and Christianity demanded is pretty rare in pagan religion: the idea people would die before doing something apparently quite harmless to themselves seems to have quite baffled Romans, and obviously ran up against their attitude of delegating imperium and expecting people to just do what they're told.

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My sense given all this is that 'anti-semitic' is not hugely helpful as a label if it's taken to imply Rome had some specific problems with Jewish people as a race or Judaism as a religion. But Rome was violent, believed in its right to dominate and command, and was quite content with collective punishment at all sorts of levels (think decimation or the rule that if a slave murdered his/her master all the slaves in the house were executed), so not 'being anti-semitic' doesn't mean not imposing awful, targeted violence on Jews.