Pardon the text wall, and also pardon the lateness of the post, but I wanted to flex the bit of time I had spent in the SJW Newspeak rabbit hole and I saw this was as good a time as ever to give it a shot.
'Syndeboy' defines a boy who identifies as syndegender - the feeling where one knows s/he is a certain gender but feels a strong affinity to traits of the opposite gender (eg. a boy who feels strongly about femininity and who isn't trans). Thus, a guy with feminine interests. That is, if Tumblr is as good a source on MOGAI as I hope it is. The initial morpheme synde- is too opaque to figure out.
'Bigender nonbinary' is a clusterfuck to try and decipher. Basically, it means someone identifies as both genders whilst also identifying as off of the gender binary. To put it into easier terms - bigender nonbinaries are attention-whores.
'Lesbian with male pronouns' is basically just a butch dyke bitch who wants to go by he/him.
'GNC gai' is shorthand for gender nonconforming something-or-other. I can't decipher what gai, whether it's an initialism or a bare word, means.
'Demiboy' is basically someone who partially identifies as a man regardless of their birth sex, meaning they may (or may not) identify as another gender to go alongside it. It sounds to me like an equally retarded way to say a man with feminine interests or a woman with masculine interests.
'Genderfluid autigender' is a mouthful, honestly. Genderfluid refers to a gender which waxes and wanes over time, constantly asking and thus enlisting the requirement that others ask what the individual is feeling in that moment. Autigender is, according to LGBTA wikia, "a neurogender which can only be understood in the context or being autistic[, and] is a gender that is so heavily influenced by autism taht one's autism and one's experience of gender cannot be unlinked." That is to say, 'genderlfuid autigender' means that the individual's gender not only waxes and wanes but also is intrinsically linked to their autism.
'Gendercute' is an "aesthetigender" where the individual's gender fits in their deifnition of cute.
Fuck these bastards for slotting personality traits into """genders""" and """gender theory""".