Pick the conclusion you want and you'll find a plethora of "science" to support it.
The reason it seems like you can always do this nowadays is that some journalists and politicians ignore the scientific consensus and cherrypick either problematic or unsupported articles. For the most part, this isn't a science problem, it's a media problem. There are certainly some examples where there's not a real scientific consensus (probably some economic issues, for instance?), but to my knowledge there's no real disagreement in the scientific community about the fact that universal vaccination would be a good tool in the fight against the pandemic. That said, the situation early in the pandemic definitely gave science a bad rap: the world changed so quickly and we had to respond quickly, so policy was made partly using guesswork and partly for badly communicated reasons (e.g. don't wear masks because we need to save them for healthcare workers). Some of the guesses turned out to be wrong, understandably, which has given people a lot of fodder for criticism, even though not guessing and not doing anything would not have been a good option either.
Anyway, this hasn't seemed to be your point about vaccines, though, has it? I've taken your point to be that a significant number of people -- e.g. healthcare workers and people in hospitality -- are hesitant about vaccines and that mandating vaccines would result in these people leaving their jobs and straining those industries. That's certainly a valid concern, but it's a policy problem, not a science problem. In an ideal world, my solution to this would be to root out the rampant disinformation out there about vaccines so that less people are hesitant for bogus reasons, rather than reasonable ones specific to their situation, whatever those may be. However, I'm sure people pushing for the mandates are thinking "there's no way we can accomplish that in this environment, and we need to fight the pandemic NOW!".
I guess I'm posting all this because I get a bit amped up about "both sides"-ism nowadays, for instance because of the climate debate, which is one of the most extreme examples where science supports one end of the political spectrum. The consensus in the climate science community has been dire for decades, and one party has been consistently downplaying the risks. It's only in the last few years that they've started to even acknowledge that climate change is real, and that humans have a role in it, though there's been no real question about that in the scientific community for ages now. It may be literally true that you can find "science" to support whatever opinion you want, but when one opinion is supported by 99% of papers and the other is supported by 1% of papers, that's not parity. Anyway, this isn't so related to your point about vaccination mandates.