People said the same thing about the US's ban on thalidomide until it turned out they were right.
In this case I'm ok with a little conservatism on the part of the FDA. The US is already in 4th place on vaccinations per capita, just barely behind the UK, without either of those policies.
Copying from my comment below, a bunch of other examples of times when the FDA was right and European regulators were wrong:
https://en.wikipedia.org/wiki/Lumiracoxib -- Approved in Europe, not the USA. Withdrawn from sales due to side effects.
https://en.wikipedia.org/wiki/Zimelidine -- Same.
https://en.wikipedia.org/wiki/Tolrestat -- Approved in Europe, failed stage 3 clinical in the USA
https://en.wikipedia.org/wiki/Rimonabant -- Approved in Europe, failed in the USA, withdrawn worldwide because the side effects were so bad.
Thalidomide is just the most famous because it was the most disastrous, but there are plenty of others.
The FDA has a strong many decades track record.