pretty sure, and as others have noted, smell is probably the primary sense. i have a couple female neighbors she adores, and when they're nearby/coming home, she whimpers excitedly before i can hear anything. on the other hand, with a couple male neighbors she's slightly worried about, she'll do more of a grunt/growl.

but visual, and even auditory, cues are also used. size, posture, stance, and gait, are all pretty good (but not perfect) indications of human gender. she's alerted on ambigously dressed people over 100 ft away who were walking in a lumbering/macho way, but ignores or sometimes wags her tail for those who don't move that way.

edit: should note that sensing potential aggression/danger is probably a large component of this behavior too.

Almost certainly by smell.

I'm a trans woman, and when I started hormones, one of the first things my partner noticed was that my odor went from overpowering and musty to just kind of "stale". I can get away with wearing shirts 2 or 3 times between washings, or go without bathing for a day or two. That was definitely not possible before hormones (at least without offending the people around me).

So I'd say yeah, if even humans can tell the difference in most cases then a dog definitely would.

Probably scent, that's one of a dog's major senses. Not sure if it's the prevalence of perfumes or natural compounds.