@MissMuffet - I can understand why you wouldn't want to see your guy fighting, whether in a ring or on the street. But i am guessing that he was already attending a mixed martial arts gym or training school when you met, right?
So I suppose I'm saying that you have to respect the skills he has and his decision to practice this sport. So long as he is not involved in some extreme form of it, and wears the safety equipment recommended, he will be fine.
I know several people who are against any kind of violent combat type activities, and they probably wouldn't date an MMA enthusiast! It's your call as to whether your issue is with the activity per se, or with him being vulnerable to injury.