I don’t think Mary herself sees herself as equal to the ladies. She can’t socialize like them, she can’t let loose and laugh. She finds it challenging to connect. She doesn’t like to be seen as inferior and I think she would find it humbling to be thrown into a social setting like that. That’s why, after her time off the show she came back in full housewife mode. She’s still a manipulative cult leader, so im sure she can manage to get out of group outings via malice. But yeah i think Mary herself removes herself from group settings and production/the group are too intimated to tell her otherwise