A lot of people like to be a bit silly with cute animals, and that's fine. Pretending to talk with them, sending cards, etc. can be cute. But there is a line that can be crossed where it just gets too much, and then it is weird. This line is in a different place for everyone depending on how used to the cutesy animal stuff they are. If one person is acting in a way that another person sees as just plain odd by being over the top, at least in their eyes, then I think it isn't rude to let them know (politely and discreetly!) so that they don't keep on making an apparent fool of themselves in front of their friend/relative.
If person A is acting in a way that person B thinks is pretty crazy, it is perfectly polite of B to let A know this to stop A from further embarrassment. A might instead find out years down the track, and feel awkward over the fact that they didn't know that B thought they were being weird the whole time. And perhaps B could just never tell A, but that's quite dishonest if it's a big enough thing to either of them (e.g. if A does it a lot). Dishonesty about big things can be fine, but not if you want to consider yourselves 'friends' with someone.
I usually just laugh it off when it gets too much, and say something non-committal like "don't be silly" or "I think that's a bit much now *chuckle and bean dip*". Most people get the hint.