The meth is what's causing this behavior. I've never touched the stuff and sure as hell don't plan on it However, I've heard from people who did that it causes a person to basically lose complete control over all sexual impulses. This effect gets disastrously worse and worse the more strung out the person gets. It also makes the person's sexual desires increasingly perverted and bizarre as they keep using it.

However, that is no reason why you should subject yourself to the cheating and the possible STDs. A meth head that has reached the point of doing things like this is most likely sleeping with NUMEROUS people. So, yes I would very much advise you to break up with him right away. He has already reached a serious level of perversion in his urges, which also tends to happen with meth heads.

If it is at all possible, get him to rehab. Yes, break up with him, but if you can get him to check himself into rehab, do it. Even though he hopefully won't be with you anymore, a person in that perverted, strung out state is dangerous to other people. He could be spreading STDs to numerous different people.