How far is too far with rescue stipulations on adopting?

I think you are over reacting. It is doubtful that using Parelli methods will be a prerequisite for adoption. Just sounds like they are trying to relate that the horses have been trained using a natural horsemanship method. Just because they use Parelli methods, it would not be reasonable to require everyone to prefer this. A professional organization will not be that prejudiced. That said, personally, I do not feel that the requirements can be too strenuous for horse adoption. Too many rescued horses are awarded to morons. So if this facility has a good screening application, it is all good. What matters is that the horse gets a proper home.