The term baby daddy is extremely disrespectful unless it's joking, and that's only if the person enjoys the joke.
You don't have to be a married person to be a legitimate father, it diminishes the family unit to treat committed domestic partners as less. The children don't perceive their parents as less because they aren't married until they start experiencing societal pressure. I remember going on a holiday with a church group, we were sole parent family, one of the married women said the larger rooms were for families. Mum was like wtf, we are a family, how dare you say that. It's sad people think like that, like there's something missing unless you conform to a standard.
I was often suprised at how my family was viewed when we weren't married, having a stable secure family is a much larger commitment then just a wedding day.