I think that most people will be sympathetic to your problem if they know about it, and most of those people will do what they can to help. Therefore I think it would be best if you made the allergies known before people turn over their tops to you. It would be extremely helpful to them if you could tell them what they need to do to prepare the tops for you. If someone told me that they are allergic, I would know that my quilts have pet fur/dander on them, and I would withhold the quilt unless they told me what I should do to clean it up. I would be too worried without specific instructions.
If you can figure out what needs to be done to the tops to make them safe for you (washing? lint brush?), then you can say that you can only take tops that have been washed/delinted/whatever.