[s1artibartfast]

Are you sure you aren't thinking of a closed shop?

My understanding is that closed shops where you need membership to apply are illegal, but union shops (post-entry closed shops) are legal in states without right-to-work.[1]

That said, I was wrong before and may be wrong again. It is really hard to understand the specifics of union law as many sources are sloppy with their terms and there are state-to-state differences?

https://www.thebalancecareers.com/what-is-an-agency-shop-vs-...

PS, I really appreciate your use of "You're confused". It is much more polite than some of the contradictions people use.

[pseudalopex]

"Full union membership thus no longer can be a requirement of employment. If a new employee refuses formally to join a union and subject himself to its discipline, he cannot be fired. Moreover, no employee can be discharged if he initially joins a union, and subsequently resigns."[1]

[1] https://caselaw.findlaw.com/us-supreme-court/473/95.html