"But there are clear and compelling arguments that vaccines aren't safe,"
No there are not.
Overall, they are exceptionally safe. When you combine the fact they are reducing potential disease as well and then compound that because of the externalization of the viral spread of such diseases (one infection creates multiple more) then they are exceedingly safe.
And where there are 'issues', they are not in the range of the ridiculous conspiracy theories thrown about.
The anti-vaxxers, especially celebrities, are a serious threat to public health.