Birth mother is offensive, when used to talk about a child's involved mother, or BF for father. Of course it is.
My DD has a 'step mother', technically. They've never met her, nor are they likely to. She is married to the man who is DD's 'birth father'. He hasn't seen her since she was just turned two. She's now nine years old.
If (in an imaginary universe) he was in her life and being her father at all, I would call him her father and DH her SF, but as it is, DH is her Daddy (he has PR) and her bio father/birth father is just that.
I have a visceral reaction to being described as the BM of my babies, regardless of how much input their fathers or step mothers have. I am their mother. NOt step, not birth, not bio. Just mother.
Even if DH described me as the birth mother of DS2 (our shared child), I woudl find it horrendously insulting. It's a term used by adoptive parents to describe absent parents.
DH has earned the 'Father' handle by being 100% of my children's male parent. If they had other involved fathers, he'd be their Step father.
That is all.
Oh, and cunting gobblychops with a dollop of fuckeroo and wankmeister.