You have an interesting definition of 'prudes'.
Anyways, I skied alta for 4 years and i've ski with snowboarders many times in my life, I don't think snowboarders would like alta. You traverse to 90% of the good terrain and 50% of that time the traverse is flat as fuck and you have to push with your poles or side step. Also, the majority of that terrain ends in a long flat section so you can get back to the lifts (some short, some long depending on how far you traverse in the first place).
Alta really isn't that big either, its probably 1/3 the size of snowbird, there are 7 other resorts within an hour, 3 of which are in the same zone that allow snowboarding, just go somewhere else. The fact snowboarders/random other people make a big deal about alta not allowing snowboarders just make its worse, if you just ignore it and stop worrying about it there won't be a problem.