Baby daddy 😴

Just a question: Say me & my baby's father was to break up after our daughter is born.. I told him I don't want my daughter around any of the girlfriends he were to have because I don't want different girls in & out of her life. (Just like he wouldn't want different men around his daughter) He said that when he would come get our daughter his girlfriend is going to be around her & he doesn't respect that I don't want that. Am I over reacting saying I don't want his girlfriends around my daughter or should he just respect that as I would respect his wishes on not wanting my boyfriends around our daughter?

***UPDATE*** : our daughter isn't born yet I'm only 32 weeks, we're still together.. It was just just a conversation that got brought up.