The only way an MMA fighter has a chance against a shaolin monk is if the fight is fought with MMA rules, in a MMA ring. Even there, as long as the monk understands the rules and had time to prepare for fighting under these rules, 9 times out of 10 he would completely destroy the MMA fighter in no time at all.
What's an MMA fighter? Someone who trained to win MMA fights.
What's a shoalin monk? A warrior trained to kill enemies in real combat.
How intensely is an MMA fighter trained? Casually during his youth, often starting only in teen years, usually in one discipline, for a few hours per week
How intensely is a shaolin monk trained? Every single day since the age of 6, doing nothing but prepare to kill enemies that attack in the night, in brutal inhumane fashion that by our standards would be nothing short of child abuse
People are immensely overestimating the fighting ability of the average MMA fighter. Most are only "master" of one discipline, which really they have "mastered" to about 10% of the monk's mastery of Kung-Fu. And are completely misjudging the fighting experience of both. A lot of MMA fighters have never been in a real fight (aka no rules, no judge) against another toplevel martial arts practitioner - they are used to fights that are interupted ever 5 minutes for everyone to have a rest, where you can call on a judge to halt the fight if you get something like an eyepoke or balls-kick, where the most efficient techniques are prohibited because too dangerous, where attacking the most vulnerable bodyparts is not allowed,... . Shaolin monks, on the other hand, spend a good deal of their training beating the snot out of eachother in true freefight.
The difference between an MMA fighter and a Shaolin Monk? The MMA fighter doesn't like getting kicked in the balls so he makes a rule not to kick eachother in the balls. The Shaolin Monk doesn't like getting kicked in the balls so he learns to freaking deal with it and fight through it. The MMA fighter doesn't like getting headbutted so he makes a rule not to headbut eachother. The Shalin Monk doesn't like getting heatbutted, so he spends a good deal of time breaking walls with his head. Fact.
*Fight starts - GSP rushes toward monk - monk headbuts GSP - GSP's face melted to the back of his skull*