That's a pretty big "despite."
Look at the current sack of shit and his administration that presides over America. Look at it knowing full well that this asshole started his campaign with racist remarks and dehumanizing latinos (I say latinos in general because of the racially charged incidents that have taken place involving American citizens in full view public since the trash took office). And then came more lies about his wealth and the reason for obscuring tax returns etc. Then came all the talk of what a pervert he is with regards to younger women at the pageantry. Despite all of that he won 68 million votes and Electoral College pushed this asinine filth to power.
Do you really believe if half of that were true for an equally vile female politician (especially the sexual stuff) from the Republican party, she would have gotten far let alone become the president?
Also, the social totem pole for Americans for leadership position in public view generally goes like this:
1. White christian man
2. White christian woman
3. Non-white christian man
4. Non-white christian woman
5. The rest
Tulsi Gabbard (iirc) is multi-racial. Lest we forget the times where Obama had to contend with fictitious birther bullshit (which Trump the asshole dolt was also part of) the same purity test bullshit would be expected to be thrown her way.
But as aforementioned, she is a right wing democrat and the country could do without one in the coming few years as the overton window has already shifted significantly to the right.
Harris has a real shot at clenching the primaries. She won't be getting knocked out of the democratic primaries for being female.
I guess we shall see.