Maybe you should just stress to your athletes that they shouldn't be adding people they don't know/making their profile public. It would teach them more than kicking them off a team, because they were drinking at a party, ever would. Kids should have their profiles entirely private regardless of the activity the participate in, allstar cheerleader or not. There are so many creepy people out there, and timelines plastered with girls in sports bras and booty shorts is gonna have creepers flocking to their profiles. Cutting down on athletes adding fans would definitely make the pictures easier for a gym to tolerate because people around the country who've never met them/are fans of the gym won't see the pics.
Plus, when they get kicked off the team they're just gonna have more time to drink and poorly represent your gym. I don't think a coach should have to deal with an athlete constantly having pics of them trashed at a party being made public to the world, but I think it is SO WRONG for a gym to police every aspect of an athlete's life when it has no direct effect on the rest of the team. What I do on my time (especially when pics aren't posted) is none of my coach's business unless I'm showing up to practices or competitions affecting the rest of the team. The gym isn't a parent. And coaches shouldn't be responsible for monitoring athlete's profiles. You're all acting like this would be something easy to police and monitor. If you kick your level 3 base with a janky tuck off, you better be DAMN SURE you're center flyer on your worlds team with a toe full and an arabian to double doesn't have a single picture posted that one might question. What if your gym has 30 teams with 10 different coaches? Suzy is buddy buddy with Coach Paula, so he just tells her to get rid of the picture and she stays on the team. Mary has an almost identical picture, but since Coach Nancy isn't as lenient as Paula, Mary gets kicked off the team. The only thing instating a 'no tolerance' policy with drinking pictures would do is cause more stress for coaches, and more pissed off athletes.
Make profiles private and instead instate a rule that they must know every person they add, and that THEY can't post pictures that could be controversial. Then, have a coach look out for pictures posted on their profile by their friends/etc. , but if one arises then just ask them to untag themselves. Kicking them off the team for something they had NO CONTROL over is absolutely insane. Kids who post those types of pictures usually have many friends and active social lives outside of cheerleading. If you tell them they can't hang out with their friends if one of those friends MIGHT post a picture of them with a Natty in their hand, well then you're asking for your business to fail.