i don't think wearing a mask is a good solution, because you would still be bringing all that pet hair into your home. At some point you would have to take off the mask, and then some of the hair would still be there to cause you problems.
I am not allergic to dogs, but I would not want to bring a quilt top with their hair into my quilt room either. I certainly wouldn't want it on my longarm. I think it's up to the piecer to give clean, pressed tops to the longarmer, especially when you're donating your time.
I don't think washing a top is a good idea, and it would then need pressing before quilting. Even then I'm not sure the pet hair would be gone, just moved around.