You can say NO as much as you want, think about it, it doesn't make you right!
I only wrote what I can see. The cupboards have dish racks in them. The rest was speculation, which is better than anything you have offered.
Lots of pet lovers are not concerned about catching germs or bacteria from their pets, because they know where they have been, not that I would share utensils.
Sounds like you are a germaphobe.