I think the lack of any sort of contract should be a bigger red flag... I'm quite sure that I am legally required to have a contract of some form saying what services I am providing in exchange for what amount of money. Not having any form of contract shows extremely poor business practices and lack of professionalism.
Personally I do not agree with 36-month contracts, without a exit clause that is too far in the future for most people. But if a gym offers them and someone chooses to sign them it's their choice to do so.
As for the original post, a contract states your obligations as well as the schools. Does the contract specify which classes you are allowed to attend?
One of my best teachers hardly charges anything for the private lessons I take. I show up, train with him in his back yard, and pay out of pocket
I've trained a number of other places, and never had to sign contracts -- but then, I mostly do private lessons given the distances involved. I do train at an Aikido school locally, but their format is pretty informal and more club-esque.
So, now that I think about it, I guess my experience is a bit biased!