Dd often has friends over & my nieces come over often too & they all don't mind the pets. Dd does go round his too but they're always in & out of the house which I don't mind at all its just I don't feel it's fair to put the cats away and the gerbil in another room for a few hours whilst he's here. Yes it's probably scary but tbh with you I'm sure it's something he can overcome. I don't understand why he's scared of all animals. He won't even go near fish!
Encourage other children round who don't mind animals. Your animals are part of your family! Could your dd play at his house more, but in the summer he and dd can play in your garden and you shut the cats inside?
We live next door to someone who's child has a fear of animals. All animals. He comes over in the garden often but will always cry & get upset when one of our pets is around. He came over for tea and I forgot that one of the cats was in my bedroom. The cat came downstairs, & the boy cried and said he wanted to go home. I pointed out to him that the cat didn't even notice him & would do whatever it liked if he left it alone. This resulted in dd now resenting our pets. we only have 3. 2 cats, one gerbil. I don't want to have to kick the cats out when he's around or move the gerbil out of his sight.