This is a great question! I think my answer would have to be that jewish characters tend to be made into extremes, in that they're either SUPER JEWISH ALL THE TIME WITH ALL THE STEREOTYPES (even when the media itself isn't trying to be offensive) or alternatively the only way you know the character is jewish is that they celebrate hanukkah instead of christmas in the winter. Of course jewish experiences vary widely, but for a lot of jewish people our culture and heritage inform our daily lives in much the same way it does for any other ethnic or cultural minority, so somewhere in the middle of the two extremes would be a lot more accurate.

In rp I rarely see jewish characters, but the few times I have the main issues have just been the muns trying too hard. Research is great, references are great, but when you go too far and start using intra-jewish terms incorrectly (think when someone goes too far playing a Japanese character and starts using Japanese slang they don't quite get, especially when it isn't necessary) it starts to be a problem. Also unfortunately I've found that some muns get uncomfortably close to fetishizing their character's judaism (usually the religious aspect) which is awkward to say the least.