I'm not sure talking to your steward would help. He's not calling the shots and you all are working as directed (her included). Take it up with your direct supe.
My personal view is that your supe is probably more afraid of an injury on his shift and views her as a potential liability.
This. Talking to a steward won't help. Talking to a direct supervisor (or
their supervisor, if appropriate) might.
And it's not to say that women aren't capable of loading irregs or any of the most physically demanding work we have. It's blatantly not true. I'd guess 90+% of women working these kinds of jobs at UPS
are fully capable. It's just benevolent, hostile, or chivalrous sexism that leads (typically male) supervisors to make decisions like described in OP. Unfortunately, good luck demonstrating that your supervisor is making not-proven-merit based decisions based on gender.