Boyfriend wants to be friends with a girl he was interested in. He says he was "really" good friends with her and that he will not talk to her but will hate me for it. What's really going on here? Am I being crazy to think this is wrong?

Jealousy isn't crazy, most of us feel it, but it's going to get you nowhere. You issued an ultimatum and now he is 'going to hate you'... which do you prefer, a bitter guy on a short leash or you uncertain that he will go astray? He could leave in either case.
Give him freedom to have friends, even women who might or might not turn into romantic interests, and just make it clear that you are out of there if they do. Then the burden is on him to decide what is important to him.

I caught him cheating on me 4 months ago with his ex. Took him back and now I'm having to deal with him trying to be friends with the girl he tried to date before me.

I just think it's really disrespectful to put temptation like that in a relationship you know?

He obviously doesn't have a very good track record and it sounds like he's adding fuel to the fire. He broke your trust once, if he wants it back, he's going to have to work for it. Though you might feel unreasonable, but you've already taken a leap of faith by taking him back. A better question is why is he still with you if he rather walk on eggshells rather than on solid ground.

Only to play devil's advocate, if you did decide to take him back, then you should trust him or at least see some progress. If you don't trust him or don't believe that he can earn your trust back, then this relationship is heading to its end whether you want to or not.