From the start of "Friends," we learn that Ross is moving out of the house he shared with his wife, Carol (Anita Barone/Jane Sibbett), who has discovered that she's a lesbian and has now taken up with Susan (Jessica Hecht). The two are going to raise Ross and Carol's child together. It's clear from the start that Carol has a good relationship with the others in Ross' circle of friends. As one fan pointed out in a reply tweet, Ross gave Carol the apartment to keep their group of friends.
This seems to imply that Monica, Chandler (Matthew Perry), Joey (Matt LeBlanc), and Phoebe (Lisa Kudrow) know and like Carol, and that there was discussion about how their split might affect their friendships. Had Monica and Ross not been related, such a conversation might have gone a different way. After all, in recent years, people haven't seen Ross' personality in as positive of a light, with critics pointing out everything from his condescending behavior and lies to his jealous, manipulative behavior in his romantic relationships. For example, in the episode "The One Where Ross Dates a Student," he ignores the power dynamic between himself and his younger girlfriend, hiding the relationship and criticizing Rachel when she dates his girlfriend's father.
At the same time, acceptance of LBGTQ rights and recognition is at an all-time high in society at large, making Ross' casual homophobia more difficult to watch. "The One with the Male Nanny" is almost comical in its portrayal of Ross' behavior if it weren't so negative with its stereotypes.
So, this theory says, without Monica's familial loyalty to her bro, Ross' friends would certainly dump him for obvious reasons.
