mismatched gender on documents

hey, it's me—another trans person! so, i've already read that applications for passport renewal with gender marker change are suspended. i'm wondering what would happen if i, at any point in the future, tried to travel overseas with my current passport, which has my gender assigned at birth. my driver's license has my current gender. i also don't look anything like the picture in my passport obviously and i don't present as the gender it says there. has anyone traveled with a passport that didn't match the gender they currently present as? does it matter that the genders on driver's license and my passport don't match?