What is offensive and what isn't is kind of a grey area. In some chatrooms "coc*suck*r" isn't offensive but in others "shut up" is considered as rude. Now, coming back to your question, Yes using "t*ts" is offensive IMO.
I have no voice, no authority in that room. Apparently I need to accept what the community decides is offensive in an extremely male dominated website, which is why I am posting here
I have to say, Yes, it's usually the community that decides what is offensive and what isn't. At the same time, just because a large number of people believe that certain comments are OK, it doesn't make those comments acceptable / valid. Even though women represent a very small portion of StackOverflow, it doesn't mean that they have no say in such matters. If you think that something is offensive, do flag it, ROs / mods will take care of it. people who continually post rude, sexist things could be suspended. If you think that a large number of your flags are being considered unhelpful, do contact a mod / RO. They will surely have an explanation for that.
So my only solution is stay away from that room when there are no responsible room owner around.
Running away from a problem doesn't fix the problem. Today, it's just you. Next week, we could have some other womanuser saying that shethey found some messages in chat to be rude / offensive. The solution that I propose is standing up to what you believe in, flag stuff if you think that they are rude / offensive - in the end you will either make this place better or learn something from your mistakes.
Is is acceptable to make jokes about tits in chat? Is this Offensive?
No it isn't. Please do note that I've had a word with the person who posted these "rude" comments.
Am I the problem?
No, you are NOT the problem here. You raised a flag on what you thought was offensive.
Does our site need to be educated to understand what is appropriate in mixed company and how to behave?
As ArtOfCode mentions, the "be nice" policy explicitly states
Inappropriate language or attention. Avoid vulgar terms and anything sexually suggestive. Also, this is not a dating site.
Bigotry of any kind. Language likely to offend or alienate individuals or groups based on race, gender, sexual orientation, religion, etc. will not be tolerated. At all.
I think this is clear enough. Before posting anything, think if some part of your comment might offend someone, if in doubt, don't comment/ remove the vulgar part. If people still post such things, then a gentle reminder (to start with) and suspension should be the right approach.
Please note that although many mods have contradicting opinions on what is vulgar and what isn't, I believe if you raised a custom flag and specifically mentioned that you found something to be rude, they would look at it more closely and do their best they can to handle it correctly.