It’s absolutely not rude. Unfortunately, your girlfriend may not care about your feelings or preferences at all. It’s so shocking to me that people care more for their pets comfort than for their partners.

There is nothing wrong with setting boundaries with animals. In the same way you wouldn’t want kids in the bed every night - it’s not appropriate to have animals in the bed. It would be just fine to put Fido in the other room with his own pillow and comfort toys.

Sleep is foundational to overall health - so be sure that your girlfriend understands that it is difficult for you to sleep with an animal. If she doesn’t respect your wishes now - you will be coming 2nd to Fido for the rest of your relationship! Boundaries are ok!