I've got my doubts. Body sculpting, explicitly including sculpting to look "animal like" existed even back in Cyberpunk 2020, which was released in 1988.
Furries were around before that of course, but the first furry convention wasn't until 1989, and furries didn't really reach mainstream awareness enough that uninvolved people started to think hating on them was cool until even later than that.
I don't doubt someone involved in Cyberpunk Red took some enjoyment in making someone who dislikes furries uncomfortable, but I'd be VERY surprised if that's why they were included back in 1988.