I thought she hasn't hung out with you and has not invited you to any social events so far, as in your original post? When has she hung out with you or is this all just when you're both at church?

Honestly I think you're making the friendship more than it actually is. she sounds like she's cordial and "friendly" in certain circles but leaves you out in events that matter.

Also she's using "friend" loosely IMO. her actions speak very differently, especially pointing out that you don't need to be at every social event with her which is going out of her way to state that you're not welcome in her social circles to me.

I know it stings but until you accept it for what it is you are going to have a hard time moving forward and past this and find real friends.