It's really shaky to say "religions" don't oppose vaccines because religious interpretation (and personal interactions with their god(s)) is up to the individual.
But it's all irrelevant in this case because Google is almost entirely an at-will employer. They can change the terms of the agreement at any time - take it or leave it.
I respect more the position of an individual saying he doesn't want to get the vaccine because of his personal convictions than because his religions tells him so (although, to be clear, I think both are stupid positions).
Hopefully Google will only allow exemptions based on health issues.
My employer mandated vaccines. Exceptions for sincere religious belief or documented medical reasons. I didn't want the vaccine but I wasn't going to lie about having a legitimate religious reason for it. Some people will, but most people wont.
So I got the shot, but if I have any serious side effects I will certainly be contacting a personal injury attorney.
If I recall correctly, there are ways to ask for religious exemption to some of the requirements (e.g. vaccination when immigrating, answering "no" to an immigration question about willing to bear arms for the US), but they require establishing proof that you have been a member of a religious community that has rules conflicting with the mandate - it's not as easy as saying "it is so because I say so". Depending on how enforcement will happen, it may be possible to at least reduce the loophole.
It will be abused, but hopefully at least some people might feel ashamed at such abuse and not go through with it when they have to do so on an individual basis.
Vaccination isn't an all or nothing game. Every single bit helps. Some people will always opt out one way or another, but that doesn't make the entire policy useless.