I don’t think there is much relation between a community using a language with no genders and its transgender population size. Take China for example. The nouns in Chinese are not gendered, and the pronouns used to be gender-neutral until about a hundred years ago when “她” (she) emerged. There are few transgender people in China, partially due to the fact that they are not officially recognized, but I don’t think there would be many transgender people in China even if the government legally allowed it.