Is it right for me to report my coworker for making crude jokes?
What sort of jokes are they?
The jokes are insulting to women and they make me think of my ex.
While crude jokes can be amusing, there is a right time and place to tell them. If your coworker has been making crude jokes at work, that is very unacceptable since employees are expected to remain professional while working. It's appropriate for you to report your coworker as his sexist jokes will negatively affect any woman working at your workplace.
But what if he gets fired?
I don't think you should be concerned with that, because those types of jokes are not appropriate for work. If his boss or HR decides that what he's done is so bad that he deserves to be let go, then that's their right.