> I think union membership rates have been dropping due to the fact that companies have been increasinly more anti union.
Contrary to popular belief, companies have incredibly little power in that regard, especially when you're talking about an already-unionized closed shop (as opposed to a company that wants to prevent its workers from unionizing in the first place). Legally and practically, it's incredibly difficult even for union members to decertify or deauthorize their union, and companies are basically forbidden from taking any part in that process. The NLRB is incredibly strict on this; both the NLRB and the courts bias heavily in favor of unions if there's any evidence that companies are seen to be interfering whatsoever in the process.
But beyond this, it's not as simple as "companies have been increasingly more anti-union" because this increaseingly anti-union sentiment comes from the union members. We know this from direct public polling, from their actions on the ballot at union elections, from their actions at the polling booth in government elections, and from what we can see of internal politics with union governance.
To put it another way: if it were easier for union members to decertify or deauthorize their union without getting fired[0], we'd probably see these elections happening more often (both successful and unsuccessful ones). Instead, union members support laws which allow them to bypass this process.
(Note that, after accounting for race, union members overwhelmingly voted for Republicans in the last two election cycles, despite the unions themselves endorsing union-friendly Democrats).
[0] Even if they manage not to get fired in the process - which is totally legal for a union to do, unlike a company firing an employee for supporting a union - the NLRB can overrule the results of the decertification or deauthorization election, which invalidates the whole process.