It’s not ANTI-union to want the basic principles that apply to elections of any sort.
It’s not ANTI-union to want to have the right to get a job in South Carolina. At Boeing.
Private sector unionization is a legitimate counterweight to the power of private employers, particularly before the era of legislated workers’ rights. Public sector unions generally capture their counterparty negotiators, which leads to abuses, but that’s another story.
The right to privacy is one of the rights that liberals, generally, also support. So it cannot exactly be called a conservative position.