DS is only 3, so of course I invited all the children from his kindy to his party, and in fact his best friend is a girl.
But I wonder about when he is older. I'd like to think I will encourage him to invite girls to his parties also, no matter the theme (although I'm not really into themes and prefer to mix it up, but DS may be as he grows). Even if he says "I don't want smelly girls to come" I think I'd probably hit the roof and tell him to change his attitude! I'm just like that.
I hate gender stereotypes but of course it exists everywhere.
I always mixed with both girls and boys at school and throughout my adulthood. It wasn't until I met my ex that I was suddenly in a situation where the boys did one thing while the girls did another thing. I hated it! I didn't get it.
I am of the feeling children should be encouraged to befriend others based on their qualities, not their gender - but of course like I said DS is only 3 so I haven't been through this gender stuff yet.