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USA elected Trump president, so anything and everything is humorous.

It all depends which group of people you talk with, I found that jokes about politics and religion do not go over well with most republicans, most democrats do not mind jokes about politics and I could even tell jokes about religion with most of them. It also depends if you are in a big town or in a village. Jokes about ethnicity are touchy as well with most groups. In general it is not as easy to make jokes about almost every subject as it is in Western Europe but that is my experience. I am in a atheist group with highly educated people in the US and with them almost anything goes.
For comedy shows etc best to look at local news or TV programming

Anything is funny if delivered to the right audience, obviously the people who have responded so far want to instill ill will, fear or generally make you uncomfortable. Botgh republicans and democrats have a sense of humor.  RTHat's thwe dumbest thing I have heard so far when it comes to people wanting to cause discord.
Ellen Degeneres is a well known and well liked comedian, has her own show, and Jimmy Fallon is as well.
Comedy depends on your taste. I agree that religion can be sensitive and in this day and age of hyper sensitivity, where everyone is so easily offended, you need to be careful. Older people are less sensitive than younger ones, they seem to know what a joke is.
Many younger people take themselves and their opinions oh so seriously.

There is no one "American sense of humor". It's a very diverse country with 320 million people and many different attitudes. What one person finds funny, another may find offensive. This is an impossible question to answer.