I think I would have a conversation before I packed my crap and left, personally.
There’s a lot of leeway between “can we not have a bunch of people randomly hacking in the ring during lessons” and “you may never ride your horse except during a lesson.” I think I’d search for that leeway if other things are to your satisfaction.
I rode in my dressage lesson yesterday in our smallish indoor with three other riders, one of whom was having issues with a difficult horse, and a person lunging. I understand how it happened as everyone including trainers were trying to get done and out of there by lunchtime, but I’d be pretty damned unhappy if that were happening all the time.
As it was, we are all friends and all acknowledged that this was an unusual event and an opportunity to get some warmup ring practice in, but none of us had really productive rides.