Well there are known redlines in each culture, and more nuanced ones for sub-groups within each culture. But if someone clearly tells you I find so and so offensive, please don't do it, and you continually do it, then you're flaming tensions and fires between peoples.
So for example, all jews find it offensive to belittle the holocaust, so it's now law in most countries around the world to belittle the holocaust and a lot of anti-semitic laws, due to violent European history towards the jews.
In the US, you have to be very careful about using things like the N word or you'll end up in trouble pretty quickly.
It is well known that Muslims are deeply offended by inappropriate portrayals of their Prophet, so it's fair enough if they request that offensive images are not disseminated. The treatment Muslims are currently receiving in Europe has many parralels with what the Jews copped in Nazi Germany. Offensive cartoon portrayals of Jews were widespeard in Nazi Germany - soon enough there were anti-Jewish street protests, similar to the anti-immigrant/anti-Muslim protests being held in Germany of late. We all know how it ended in Germany of course.