Clearly, they're insane.
Nicaho? I can totally see you back here in the future, wanting to dictate whether or not the child can hug her step father. Whether he can attend sporting events, whether HE can go to the daddy daughter dance with her at HIS church (or whatever).
You HAVE TO LET GO of this. You'll drive yourself and everyone else mad.
Let me tell you this. I called my step-father by his first name, and I call my Dad, Dad. My Mom married my SD when I was 6. He was a daily presence in my life, and until he died last year, I loved him more than any man I've ever known. I love my Dad. And I have an important and close relationship with him. But my step-dad? He was my "daddy" even if I never called him that. The affection and the actual relationship was not dependent upon a word or a name.
Make this a hill to die on, and you're just setting yourself on a path of control and pettiness that is NOT going to strengthen your relationship with your child. I promise you.