The "grammar" is gender-neutral only in the sense that there are no morphological markers for gender (or for that matter, for number), but the speech itself is very heavily gendered. Different pronouns, different verbs for the same meaning, etc.
Discussion
Sure...I am just a beginner, and don't get all the nuances
But from the interactions I've seen on here, it's not easy to figure out even amongst Japanese speakers whether some user is female that easily...I maybe wrong but that's the sense I get.
I can guarantee you English is A LOT less gendered. In Japanese even the first person pronoun is different based on gender.