will genderqueer peoples children be genderqueer?
Occasionally yes, as far as I know there is no evidence that gender identity is heritable, but particularly I would not expect it to be anti heritable, that is, some gq parents will have gq children in the same way that some people who are prom queens will have children who are prom queens.
However if the question is restated as is it more likely that gq parents will have gq kids, then the answer would have to be something along the lines of possibly, at least in the fact that the way we express gender changes thoughout time, and having parents who know that gq exists as an identity means you at least know what the words are. I think I would have known I was trans a lot earlier if I knew trans guys and gender queers existed, if there where models of gender which fitted my experience.
Other than knowing it exists, then no, I expect it probably isn’t heritable, but that is just a guess and if someone wanted to research it, I would kindly suggest that they research something that would actually help trans people, rather than research that all to often sets us up as a defect.