Wow. Everyone responding is so understanding. Maybe the ladies in the group will be too. I will talk to the coordinator about the issue.
Perhaps it will be alright. That is if there's anyone in the group that doesn't have a pet. And if we can keep track of where the tops have been. Sometimes the cloth comes from several people and the tops get worked on in various locations.
My other approach is to just do the whole process from start to finish. I'm a prewasher for this reason. I could make a list of all the charities that I could make quilts for and just do it on my own.
I really appreciate all the responses. It's given me food for thought. I don't feel so weird and like I'm putting people out for being this way.