The FDA is expecting to issue full approval by labor day, so I'd imagine pretty much everywhere will start to require it then.

As for legality, it seems that there is pretty solid precedent for an employer to require vaccinations. Plus you can bet that United wouldn't announce something like this if their legal team weren't pretty confident it'd hold up in court.

Now I'm sure there'll be waivers and exceptions, but since I imagine most other countries will require incoming foreigners to be vaccinated that'll be more complicated.

I find it hard to imagine an airline giving non vaccinated crew members a special domestic bid option, but who knows.