Just by the sheer number of very overweight CM I've seen on my many trips, I'm pretty sure they aren't discriminating against that. Although I will say that I have noticed an increase in the not so attractive CM in the not so attractive working locations...
Men can have very neatly groomed mustaches. Sideburns have to look a certain way, sizewise - no more than a certain length, hair must be kept neat and above the collar, and the rest of the face clean shaven. Trust me (I'm a girl) but a male friend of mine came to work with a scruffy face and he had to dry shave with a disposable razor before they'd let him start his shift. We were CPs in 2002, working at Epcot.
Same rules for us girls, hair color must be "natural" looking...so no hot pink streaks in your hair or obvious bleached highlights. One ring on each finger. One earring per ear - can't remember the rule if they had to be studs are notI always wear studs anyway but obviously we could not wear large hoops or dangle earrings. Any tattoos (male or female) had to be covered and not seen by guests. Natural, not overly done make up. That sort of thing.