MOGAI stands for Marganilized Orientations, Gender Alignment, and Intersex¹. It was first created as MGS (Marginilized Genders and Sexualities) in 2013 by Kay (@taodefensesquad on Tumblr) to replace GSM (Gender/Sexuality Minorities) due to connotations of the phrase "sexual minority"². The S for "sexuality" was changed to an O for "orientation" by Tumblr user @sxizzor (now @autisticthassarian) to "exclude cishet kinksters and poly people"³ and "gender" was changed to "gender alignment" (GA)⁴ for clarity; both changes can be found on this archived post. The current term MOGAI was created by Cloud (@cisphobeofficial) with the adding of an I for "intersex" in 2013.
Due to common misinformation, I will clarify @cisphobeofficial is transgender and disabled. A common accusation is that the creator is a p*dophile (e), however, this is incorrect as they are a CSA survivor, and were 14 at the time of coining. The term was also not coined as a joke and originated from Tumblr.