My cat can care less about anything but the crickets I feed my leopard geckos.
My Dog on the other hand..... she is hyper focused on needing to know about ANY other animal I interact with. For her, I have her put into a sit and then 'be nice'. Which means I will let her gently sniff the animal. Sometimes she gets a little bit of a nudge in, which is why I never let the other animals left alone or in a careful hold. Usually once she gets a little sniff tho she'll let me finish up my business.
Snakes are always held gently but with the first 1/3 held away from the dog to prevent any strikes. She gets to sniff the back end.
Leopard geckos, she gets to sniff the more front half so they don't freak out about a nudge to the tail.
Small pets like rats or chinchilla get a bit more freehandling while they're in my lap. She's allowed to go up to their cages and sniff them through the bars.
The only animal she's obviously allowed to interact freely with is the cat.
I would never let any other animals interact freely. The reptiles always have the cages clamped or locked when not working with them. The dog is never allowed to be any animals during feeding or my one especially defensive ball python.