This feels like a very unlikely scenario. More likely, both the employer and the union are sexist, and it's an orthogonal concern. I could equally ask, what about a sexist company, and a non-sexist union? Unionizing is a double benefit, then!
> you go and work for the non-sexist company. But then that company gets a sexist union
The union would primarily be people already at the company who unionized, so it wouldn't make sense to claim your coworkers became sexist by unionizing when they weren't before.
> This feels like a very unlikely scenario. More likely, both the employer and the union are sexist, and it's an orthogonal concern.
That is possible, but so is the other thing. And having both a sexist union and a sexist company is still worse than only having a sexist company, because their activities still overlap. The hiring manager avoids hiring women or only hires them when they're pretty or massively overqualified, the union excludes them from union leadership roles where they might advocate for maternity leave etc. while also precluding them from negotiating directly with the company, including different managers who may not be as sexist.
> I could equally ask, what about a sexist company, and a non-sexist union?
Then you would still have to work for the sexist company, about which the union may do nothing even if they're not overtly making it worse, and if they do focus on that it requires them to burn your negotiating leverage doing something about that when you would have been better off to go work at the non-sexist company. Which is much easier when more such companies exist because the industry is less consolidated.
> The union would primarily be people already at the company who unionized, so it wouldn't make sense to claim your coworkers became sexist by unionizing when they weren't before.
"The company" in this case refers to management. It's completely possible to have non-sexist management and sexist workers. In blue-collar occupations this may even be more common. It's also possible for predominantly non-sexist workers to elect sexist union bosses for reasons unrelated to sexism.
> you go and work for the non-sexist company. But then that company gets a sexist union
The union would primarily be people already at the company who unionized, so it wouldn't make sense to claim your coworkers became sexist by unionizing when they weren't before.