Does a biological father have the right to keep a stepfather away from a child?

Yes, if the father and stepmother are divorced, and if his daughter is still a minor he can prevent her from seeing her stepmother. But if the father and stepmother are still married, that will complicate things, making it rather difficult. He shouldn't expect the stepmother to leave her own home when the daughter comes to visit, and he shouldn't expect his daughter to only visit with him in public places. And if he is still married to the stepmother, then he shouldn't have a problem with her and his daughter visiting each other.

If however his ex is in a same-sex relationship and the step mom is her new gf/wife, he can not. Neither of the parents can dictate to the other one who the child sees when in care of the other parent unless that person is unfit to be around the child and that would require proof to show in court.