Gender locking romances, but not player characters?

If you want a true silent MC (MC in which is a true blank slate), check out Ace Combat series, Hollow Knight, and Undertale. Our character, despite being the main protagonist and always being invited into chit-chatteries, never have their own voice. A true robotic mannequin that only do what the player does.

Their identity is never exposed (except in AC5 where you got a screenshot of a masculine pilot, the MC, although the face is covered by its squadmate arm. Otherwise, no in-game text mentions that you’re playing a male pilot) and you may self-insert yourself into their persona.

Edit: Oh, and in ACZero, a character refers the MC as “him.”
Well, just wanted to point that out ¯\_(ツ)_/¯