Here's the thing about birth certificates..  they don't list gender.  At least, my Ontario birth certificate does not.  It lists sex.  As in biological sex.
Even if you accept gender is a social construct and so on and so forth.. biological sex, with very, very rare exceptions, is a black and white issue.  It is binary.  You are male, or female (intersex falls in those very very rare exceptions).

Can we stop with this foolishness?