The dictionary definition[1] is female parent so I'm not actually sure that the term mother would be exclusive of adoptive parents or lesbians who's partner gives birth. But looking back at it this would likely exclude trans men who give birth so I may in fact need to extract my first comment.

We're 100% in agreement on the offense issue though. I don't get why anyone is offended by what someone else prefers to be called. Take the politics out of it and that's like being offended that someone says their name is Steve when you absolutely refuse to believe they are called anything other than Bill.

[1] https://www.merriam-webster.com/dictionary/mother