I have both male and female best friends.
I'm also bisexual - so according to many here, I guess that means I shouldn't be allowed to go away on holiday with a friend ever, and possibly wouldn't be allowed to have a close best friend either, as both would be allegedly disrespectful to my partner.
In reality, friends are platonic, and are not lovers, so it doesn't make a difference what sex I'm attracted to and what sex my friends are, and whether those two things are the same or different.
And in my relationships, there's strong mutual trust, so I don't need to police a partner or to be policed, because we trust each other.
I treat my friends of both sexes equivalently (and apparently even now, this is not acceptable to many, go equality(!) ) - so yes, I would go away on holiday with both, would happily share a room and a bed with both (platonic, yes, it's perfectly possible!), and don't think it's unusual to exchange Christmas greetings with my best friends on the day itself.
@OneSassyRobin if the best friend was male, would you have a problem with your bfs behaviours? If so, then speak to him about it.
If your problem is purely because the best friend is female, then what you're actually saying is either that you don't trust him (again, inquire internally to see why that is, and address it with him or yourself as appropriate), or that you feel insecure (and again, is the insecurity because of anything he has actually done (talk to him about it) , or is it simply a product of your own fears (work on it yourself).