I’m not Catholic, so not exactly a brother or sister, but part of my reaction is due to that and might be useful.
One, I would not personally attach any symbols of my faith to any of my pets.
Two, if I saw anyone else do this I would think it was weird and superstitious.
Does it mean that the pet is considered a member or representative of the faith? Is the medal etc a talisman or understood to provide some sort of protection? That comes across as superstitious to me.
Are the animals somehow consecrated to the faith or to a particular saint? If so, what does that mean?
And then there is the chestnut “what would Jesus do” (which I know is not of Catholic origin) but I’m doubting Jesus would put a religious medal on an animal. The only thing I can think of is if the animal is somehow consecrated to service within the faith as either a sacrificial animal or carrying out some other type of service that had to do specifically with the faith, not just a companion animal.
Not that you as a Catholic should base your decisions on the personal feelings of others or what conclusions they may erroneously draw, but I do wonder, what would you think if you saw a dog with a Star of David or Thor’s Hammer on their collar?
But probably I just overthink things.