This explains the issues with GSM/GSRM and the issue with MOGII. 

GSM/GSRM

Stands for “gender and sexual minorities” or “gender, sexual, and romantic minorities”. However, proponents of the term often use it to include both sexual orientations and sexual preferences (such as BDSM enthusiasts and pedophiles). Objections have also been raised about the use of the term “minority”, and the term excludes intersex people.

MOGAI/MOGII

While not a perfect term, Marginalized Orientations, Gender Alignments, and Intersex does not have any of the issues raised with other proposed umbrella terms. Another variety, Marginalized Orientations, Gender Identities, and Intersex was initially proposed, but it was pointed out that cisgender, heterosexual female is a marginalized gender identity, so the language was changed from Identity to Alignment to clarify that the term intended to include non-cisgender, non-heterosexual people and intersex people only.

via mogai-lexicon