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 woman saying that she 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.