Can I hide my online presence?

So on my Xbox, I have my appearance set to offline. I also have it set to offline on the Xbox app. However, sometimes when I’m playing, one of my friends will get on and see that I am playing a game and get pissy that I didn’t invite her to play.

I’m not looking to see if I’m being a dick by not inviting her to a party or game every time I’m on. I would just like to know how to make sure she can’t see my online presence without deleting her off my friends list. It’s getting annoying and I am literally on an alt account because my normal reddit username is the same as my old Xbox gtag. Thanks for any help!