Does Sharing a Joke Mean You Believe It (Or Any Part of It) To Be True ?

I agree with you;

"This includes, and is not limited to, such things as using derogatory terms about ethnicity and some elements of religion."

Some years ago the big thing was the Polish jokes which were amusing to me but didn't make me believe that Polish people were any more or less intelligent than any other ethnicity. That was before I realized my sister-in-law was of Polish descent. She, an intelligent well educated, well spoken and attractive woman, was hurt and embarrased by these jokes which implied stupidity. Taking that one step further, the first time she heard a joke was one thing but endless repitions were quite another. Now I'm not Polish but my daughter is blonde so I'm now on the receiving end because these jokes (?) imply all the same things about her.

A good rule of thumb is to think of yourself as the butt of the humor and imagine how you would feel with these so called humorous depictions applied to you.

I find things humorous I don't agree with or find offensive all the time.  Just because you shared it doesn't mean you agreed.

Agreeing has nothing to do with it. The question here is whether or not you are sensitive to the feelings of others. The "jokes on you" can get real old, real fast, when you're on the receiving end and hear the same things over and over again.