An exclusive gender is any gender identity that has a certain prerequisite, often unrelated to gender, that and is required before being allowed to use that identity. Examples include being from a certain culture, being disabled, being neurodivergent, being intersex, etc. These genders may be exclusive because:
1) Some genders have spiritual/religious meanings and shouldn't be used by people of a different faith.
2) Using culturally exclusive genders without meeting the requirements is appropriation.
3) Some genders (such as neurogenders) can't be used by neurotypical people because they do not have the experiences required to be that gender.