People do have platonic, close friendships with the opposite sex. I have a male best friend.
The alarm bells here are that it is way too intense. If it was a bloke he was constantly texting and talking about, you would find that weird too - because most friends don't have that level of involvement. So it's not because his friend happens to be a woman, it is because it is far too intense.
The other alarm bell is that he is not involving you. He wants to keep you separate. Maybe he wants to give her the impression that he is still available to her? Maybe he puts on a different persona with her and doesn't want you to see it?
Whatever the reason he is keeping you separate, it isn't good. You are supposed to be one of the most important parts of his life. If he isn't making that clear to her by involving you, then he's doing it for some reason and I can't think of a good one.
So don't let him make you feel unreasonable and as if he has to choose. He doesn't have to choose, he just has to involve you and be more transparent with you both.
And he needs to dial down the intensity. I don't have many friends I speak to more than once a week at the moment. Maybe the odd text here and there. Certainly not constantly.
And if he wants to see her, he can include you. You need to meet her even once.