My friend is in almost the same position. me and her are good friends but she's dating my brother and he doesn't like us hanging out. what she does is a balance. she'll hang out with me some and then hang out with him some. try really hard not to take side. if they don't get along all that great you can asks your friends to not pick on him so much or ask you boyfriend to lighten up some that's just the way they are. if nothing works then just hang out with them at different times. but I really wouldn't recommend dumping your friends for him. a girl needs her best friends and although I don't know them or him or you for that matter I often find that your friends see people close to you through a better light. right now yours may be glazed over with the idea of romance and new love but if your friends don't think he's good enough for you then he really might not be and you might want to open your eyes a little bit more.
but I do agree with Felicity X, if he insist on you dumping your friends you should break up with him. remember your the only one who has the right you run your life, nobody else whether it by your boyfriend or your friends. you just have to open your eyes and take in everything that's going on.
also if you catch him cheating on you again I think you should dump him and I agree with your friends when saying he's not good enough for you. you can forgive someone once for breaking your heart but if they do it again then they're not worth the pain it brings.
If you wish to keep both your friends and your boyfriend, be like Nanny McPhee, who said: "I don't take sides!"
However, if he has the reputation of being "a cheater" as you put it and you know the reputation to be well-founded in fact then, no, you cannot trust him. Also, if you are comfortable with your friends' teasing and joshing, and he is so offended by it, ask yourself, seriously, whether you could really be happy with such a humourless character long-term.
Is he getting mad because he does not like your friends as such, or because he does not like the idea of you having friends of your own? If it is the latter, then he is showing signs of ultra possessiveness and could be a very unpleasant, or even dangerous, man to get close to. He could be the type who would be jealous every time you spoke to someone else, try to stop you having anything to do with anybody but him. In its extreme form such people can get obsessed with the idea that their partner is being unfaithful for no reason whatever or feel that they have to be practically kept prisoner to avoid any possibility of their being unfaithful, and when people are that unreasonable they can also become violent.
Make it quite clear to him that you have every intention of keeping your friends and, if he insists on the opposite, dump him, quick!
I say never take sides, be yourself. They don't get along so they do not have to be around each other. This is so easy for me to say because my friends don't really care for my boyfriend either. But he is your boyfriend and you are the only one other than his family and friends that have to deal with him. Do not let something so petty stress you out. Its very simple they don't have to be around each other.
The worst feeling is losing a friend over some guy... If I were you I'd dump the guy and stick with my friends.