You might not know what will happen if you are accommodating, but you absolutely know what will happen if you aren't accommodating.
^This.
Choose your battles. The venue has made their decision. You can work with that and an eye towards future work and a possible good working relationship; or you can ”stand your ground” and slam the door behind you.
Considering it’s a casual thing for your band - and you’re willing to work for what’s basically “hobo pay” it doesn’t strike me as something worth getting into a showdown over. If you had passed on another engagement, or there was serious money involved, it’d be one thing. But getting bent out of shape over something as minor as getting a night switched? Nope. Roll with it.
Note: I wouldn’t automatically assume the double booking wasn’t an accident like some here are saying. I’ve been in a few situations where a place had two owners who each booked a different band for the same night without telling each other. It happens. No need to assume something nefarious.