People use terms of endearment for their pets. They have done so throughout the centuries (Search Roman dog tombs for more information). The terms change but I believe the sentiment remains the same. People love their pets. The words someone use whether it’s “waddle puddy, fur babies, the girls, or Sweetheart” Don’t really matter, I find it very weird that some people consider particular terms of endearment offensive or a red flag.
I do understand what is meant by helicopter parenting the pets, but I think that is best sussed out in a video call or in the responsibility section of the listing. It’s been my experience that many people who refer to their pets as furbabies are neither unreasonable or overbearing. I think less word-picking and more nuance is needed.