This is pretty common when they can no longer relate to the real pet andas they progress. For a lot of women it is a doll. There are even special dolls for alz patients.
My loved one's care facility has a supply of stuffed animals and baby dolls that they use often. The residents definitely gain a lot of comfort from them.
Yes, go along with it. My mother always loved babies, and when she was in her final years, she "took care of" baby dolls, which is a similar thing. When your loved one can no longer care for a live animal, an attachment to a stuffed animal serves a real purpose.
In fact, there are very realistic stuffed dogs and cats designed for that purpose: they have built-in sensors and move in response to touch (move their heads, wag their tails, purr, etc.) Check out this link.
https://joyforall.com/
I would say yes, go along with it. You can't change how they feel when in fact you agreeing will go a long way in keeping them happy. I know it is frustrating but it is just another bump in the road on this devastating journey we are on.
Thank you very much that really helps.