"One gig in with a great start and our drummer is already whining about not wanting to play certain songs. "I don't like Poison, I don't wanna do Brown Eyed Girl, I'd rather do Obscure X".
"Everyone in the band is considered an equal."
IMO, the new person in any band should not immediately be an "equal". He's already angling to change "your" band since he's an equal.
I suggest that, since he's new, that you change the rules of the game and tell him (since he's already gone against the rules you set out) that it's your band and he's not equal anymore. You might tell him that he should concentrate on playing the songs that are picked (and that make you money) and if he has any complaints, to keep them to himself.
Imagine if he was a "new guy" at some other job. If he started telling everyone else how to do their job or complaining about the way things are done, he'd be out in a heart beat.
Nothing should be different about your band.
We're one of the highest bar tab grossing bands in our immediate area ...
You should be able to get a replacement drummer pretty quickly if that's your band's status.
Now we're hearing this sarcastic crap like "I'm gonna go watch Fried Green Tomatoes because chicks dig it".
He's a cool dude and he can play.
I don't think he's so cool if he's creating drama where none need be created. Based on what he was told that the rules of the band were before he started, sounds like he's trying to sabotage your band.
IMO, based on what you've posted, I don't think he's redeemable if he's started talking nonsense after one gig.
Sounds narcissistic to me. If he was really a team player, he wouldn't be making these kind of remarks. Remarks that sound like he likes to hear himself talk and have the scent of a "I'm not happy unless I'm the center of attention personality". The "look at what I can do" nonsense that leads no where and burns brain cells because there's no solution to a problem that doesn't exist accept for in his mind.