I agree. I think there is an absence of objective assessment of some of the stuff being deemed inappropriate. I don't necessarily disagree with trying to stamp out certain stereotypes, but those should happen when there is demonstrable harm coming from them. The stereotype of Jewish people as greedy bankers for example has contributed to antisemitism and consequent attacks on the Jewish community. That's a stereotype worth addressing. Where there is no harm occurring though, those stereotypes just shouldn't merit the energy wasted on them.
It's worth remembering, stereotypes are a natural consequence of the way our minds categorize. We need to focus on when that's a problem and when it's not.
How do you recommend addressing stereotypes beyond pointing out that not everyone belonging to that particular group fits in with the stereotype? If by addressing you mean trying to silence or cancel anything that includes the stereotype or declaring the stereotype to be false when there is evidence that it is based on truth, I don't agree that that's a good idea.
Stereotypes can lead to violence but so can facts. We don't or shouldn't get rid of facts for that reason. Instead we need to remind each other that even if a stereotype is true we shouldn't over generalize because people are individuals and don't always fit into cookie cutter molds.
For example, in this case the stereotype of Jews as greedy bankers comes from the fact that Jews are over represented among greedy bankers and tend to be good at acquiring wealth in general. You can verify this through your own research if you want and you will see it is often the case that jews are heavily over represented on lists of most wealthy this or richest that. You'll even see Jews admit to this, for instance I had a jewish roommate at one time who told me that jews only care about money and his community looked down on him because his business ventures had failed and he was poor.
However, when I was in middle school my best friend was jewish and he wasn't greedy about money and his family was pretty down to earth as well, so clearly not all Jews fit into this stereotype.
It's like this with all stereotypes. They are almost always based on truth. Occasionally you might run into some false stereotypes, usually because they are either outdated or based on a misperception but that is the exception. The norm is that they are based on some truth.
I am Italian American and Italian characters in TV/movies are often based around either mobsters or chefs. It is true that there are Italian mobsters who have been very powerful in parts of Italy and it is true that Italians love good food. However my family has never been involved with any sort of organized crime to my knowledge, although my dad was at the same business dinner as a mafia captain at one time. I am starting to get off topic now but the point I am making is that in my view the way to reduce harm associated with the stereotype of Italians as mobsters is not to deny the existence or influence of Italian organized crime but rather to point out that the majority of Italians are not a part of it.
I think stereotypes are actually a positive thing, in that they represent a set of impressions we get from a group like a caricature. A caricature isn't supposed to look exactly how the subject of it looks, but rather is supposed to exaggerate the subject's unique features in order to show how that subject may appear in the minds of others or emphasize what stands out about them. I think it's actually very cool that we have the ability to do this and it takes skill to craft a good caricature just like it takes skill to observe people and then create a stereotypical character based on what you noticed. So much comedy involves this. Most of the characters on the Simpsons are stereotypes of one thing or another, which is what makes the removal of Apu seem to go against the core principles of what originally made the show funny.