I just returned from a 3 week tour visiting about 15 states and 3 seasons. Yay America. Most of these shows on this run were on college campuses. I do a fair amount of college shows. They're fun. They pay well. And the audiences are mostly very attentive.
However, once in awhile there will be a couple drunk assholes who show up. Not often, but occasionally. This actually happens more often in the club scene. I'm sure you've experienced it. The bros who yell "Free Bird" like the joke didn't turn stale in 1997. The loud (drunk) girls screaming for Bruno Mars covers. Oh drunk people.
But then there are the more subtle assholes. Like the dude with his back to you at the bar carrying on a loud conversation, totally ignoring your set. Or the woman asleep in the front row at your listening room concert. Or, more commonly, those starring at their damn phones the entire time. I've seen it all.
My first instinct with the loud assholes is always to engage. Sometimes you have to. If they're making themselves a part of the show (like yelling at you or talking loudly disturbing the show for others) you have to engage. It's awkward not to. BUT you don't have to do what they say. Actually, you should NEVER do what they say. It only encourages them.
There's a huge difference between taking requests from fans and appeasing drunk assholes. Drunk assholes are just there to party and make themselves look cool around their friends. Unless you're a cover/party band, these people are not your crowd. You don't want them at your shows. They are an unwelcomed detraction for the people who ARE your fans and are actually there to see you.
Remember, there are always people in the room who want to hear YOUR SET. They are holding onto every word you sing and every note you play. Don't play to the assholes because the show is not meant for them. It's meant for the fans (or potential fans) who are actually into your music and will stick with you for the rest of your career.
You don't win fans by appeasing drunk assholes. You win fans by shutting them up (humorously) and kicking ass with the set you prepared. If the assholes leave, so be it!
As a singer/songwriter who mostly plays solo, I've gotten very good at calling these people out. I take a 3 step approach:
Step 1:Humorously engage
If there's a loud conversation going on at the back of the room and everyone else is silently listening, I may whisper through the mic and (politely) discuss the wardrobe of the offending party until they notice and take the hint. If there is someone who is constantly yelling out requests of cover songs I may say "So I only know 2 cover songs and I already played them. However if you have any Ari Herstand originals you'd like me to play let me know!" That usually puts them to rest. Many times they'll realize that I'm not into making the show about them and they leave. Good riddance!
If the humor doesn't work (it almost always does). I may engage in a bit more assertive, albeit still polite, manner. I may look them directly in the eye with a "why are you fucking up my show" look that they will recognize, and others will appreciate. Or if they're close to the stage I may hop off the mic and ask them to stop. With a smile.
Step 3: Kick them in the head
Now, I only know of Brian Jonestown Massacre actually doing this literally. And I definitely don't recommend it. But take the figurative approach. Stop the show. Make it known that you don't like what they're doing. Get them kicked out (or ask them to leave). Florence and The Machine stopped the show because of a fight. The way she approached it was brilliant.
In my 600+ shows I've only ever had to get to Step 3 once. The entire room was silently listening and enjoying the show except for the opener (go figure) and his douchebag friends standing at the bar - which happened to be on the side of the stage. I could hear every word (as could the entire house). I went through Step 1. Nothing. Step 2, a bit of quiet, but then they got right back into it. And finally Step 3. I stopped the show, walked over to them and asked them to please stop talking. The bartender actually kicked them out (after repeatedly asking them to be quiet apparently). Everyone in the house applauded. I then made a joke about it to lighten the mood and remove all awkwardness.
You don't want assholes at your show. It looks bad on you. People come to concerts for the scene as much as the music. If your shows turn into asshole fests then the crowd you really want will be driven away. Catch this early on. Make every one of your shows YOUR SHOW. Take control. Command YOUR stage. Play to the supportive faces in the room. Play to those who want to be there. For those who ended up at your show and are working their damnedest to destroy it? Kick them in the fucking head. Figuratively of course.