When I started playing, I didn't care what condition the set was as long as there was a set, I was so excited to be able to play and of course a new kit was way out of reach for me, I was really poor. I made up for shitty kits over the years by playing with energy and making sure I made the band sound as tight as possible. now, when I can basically afford the kits I want (hence the one in my avatar picture) I wouldn't feel too great playing a crappy set, but like others said, better to beat up the venue set than yours, and I would only bring my sticks, my pedals , my snare, and maybe hats, ride and a crash. Things that you can change in less than 15 min, and don't ask permission, just change the shit, if you can't manage with that then you have no business playing... IMO.
I'm not convinced the bass player was being benevolent. I see it as the bass player thinks of you as "less than" or incompetent and that he knows better. Like a parent saying, don't listen to the child, listen to me, I'm the adult. He isn't respecting your wishes and discounted you completely. JMO, I can't pretend to actually know what he thinks. But judging from the circumstantial evidence...
Beings it is a punk gig...it might be best for your own mental health...to just let all of your concerns go and say F it. It's a losing battle. It is. If you kind of surrender to that fact, it will be the best attitude you can cop. Laugh at everything (not get frustrated) that sucks and adapt and overcome. Maybe you can enjoy yourself more letting go. No one feels a drummers pain except other drummers so a bad kit has to be silently and cheerfully worked around. Musicians attitude, good or bad, translates to the audience. The audience members won't notice the drum tone as much as a negative mental attitude if it is allowed to be shown.
Sometimes drumming is like a job in that you have to do things you don't want to. Sharing kits is exactly like wearing someone else's clothes. It's both comical and frustrating to the person who has to wear someone else's clothes. Whatever, let's play. I may feel like a hammer but the audience won't pick up on that if I don't show it. Damn the torpedos. When I have to sit at a kit where the throne is low and the snare is high....no one can see my discomfort. It looks normal to them. I try not to ruin that illusion. If you have to swallow a turd, don't chew on it, another good piece of advice I picked up along the way.
This is a suck it up situation IMO. I use Tony's top advice...shut up and play, shut up and play, shut up and play. That's easily the best piece of advice I ever heard. It particularly applied to me because I'm opinionated in a big way when it comes to music. Now I just shut up unless I'm asked. I'm never asked. Letting shit go...I highly recommend it. It's better to shut up and play than complain and play...as a drummer. You can't hold back the tide, (lamenting a bad kit tone) so accept the tide and use it to your advantage if possible. Or don't use them at all.
Me I don't even hit awful sounding toms on a backline kit unless I absolutely need to. There's always other musical options when the tom tone sucks.
larryace makes a good point about shut up and play. That said, if there are other optionns available to you, give them a shot. I wouldn't quit the current band unless you know for sure the other one will work. Which means you might have to play in two bands at once in order to flesh out the new band and see if it will provide you with some long term potential and more importantly, long term enjoyment. Of course, you'll have to have the time available to manage two bands until one comes out on top. I believe that you should never just settle if you aren't happy. At least see what else is out there. Who knows. You may find your dream band with a bunch of people who actually care about how everyone in the band feels.
If you're playing punk shows it's very unlikely anyone gives a crap how your tom notes sound. Try to let it go if this is the only band annoyance. When you can, offer to supply the kit. When you can't, just get on with the show.
I've rolled my eyes at plenty of guitar players who refuse to use a different amp or play without 30 "tone pedals" they haul out. Sure, they care about the subtleties, but I and nobody else really does.