You both have it mostly backwards. The Taft-Hartley act mostly bans closed shops and allows states to pass “right to work” laws making payment of any agency fees to unions optional.

In no state are any employees compelled to formally join a union. In an American-style “closed shops” in a non-right-to-work state, if you don’t join the union the bargaining agreement can charge nonmembers an agency fee representing most of the dues they would pay as members. Not to mention pressure tactics to join.

Also especially in the trades in major markets unions control apprenticeship programs and hiring halls and make it virtually impossible for nonmembers to get union work, as well as gatekeeping access to apprenticeship programs in the first place.