Devora, this isn't an area I feel particularly strongly about, but I'll have a go at a chat about it.
In answer to your question-;
I have not adopted myself but I have second hand experience in that a good friend has two adopted children, a boy and a girl, now teenagers but from virtually birth. My sister has fostered several children over the years, but not recently. A very good friend has a long term foster daughter. Another very good friend 'fosters' dogs as an ongoing concern, and has 'adopted' several dogs over the years.
All my three friends (not my sister) are also friends with each other. We all have dogs. We all dog walk together. My dog friend 'fosterer' is obsessed with her dogs, talks about them all the time, and it wouldn't have occurred to me that my other friends might be annoyed with the terms she uses. She does use the words foster and adopt in relation to her dogs, continually and she's involved in a rescue charity. My two other friends haven't indicated that they are remotely aware of it, and don't seem to have batted an eyelid.
Before I saw the thread I had no idea that people would resent the term to refer to animals as well as children. Possibly because my adopter/foster mother friends haven't taken offence to it.
That is my sole experience of it all.
Adopted can refer to other things as well; roads can be adopted, countries can be adopted, and I dare say other things as well. The word 'adopted' has never been exclusively used for children.
As I said previously, personally if I had a rescue dog I would call it a rescue dog rather than say it was adopted. That would just be my preference. If I was fostering a dog, I would say that, it's succinct, everyone would know what I meant, and I think that's the most suitable word for the process.
(I hope I'm not boring you.......)
Even though I can kind of see why the OP is indignant, and clearly children are more important than cats/dogs (to most people, but not for example to an elderly lady whose cat is everything to her) I also don't think she's right that her feelings matter more than her manager, or the lady in my example. (Am unsure that I have explained that bit well enough)
So whilst I have a little understanding that it might irritate/upset the OP it's all a moot point anyway. I think the words 'foster' and 'adopted' won't be disappearing from being used in conjunction with animals, particularly dogs and cats, in fact, I can imagine it being expanded to include all sorts of other animals.