My employer requires seasonal flu vaccinations (healthcare employer). Also when I got their job offer, I had to provide evidence of a bunch of vaccinations I should have received as a child. I didn't feel like finding all that paperwork so I ended up giving a blood sample which they ran a bunch of tests on and confirmed I was at the appropriate level of vaccination.
As for covid-19, employer came out saying they are not making covid-19 mandatory for 2020-2021 but who knows after that. Normally vaccines are tested for YEARS. This one was obviously not. Also, Pfizer and Moderna are using a new-ish type of vaccine tech called mRNA. I'm very concerned about taking a vaccine with new-ish tech and with very little testing. We don't know what the long term side effects are years from now.
A huge personal concern for my wife and I is there was zero testing done on women who are pregnant or women who become pregnant shortly after vaccination. Wife and I were having conversations about starting a family right before the pandemic hit. We put those plans on hold indefinitely since the world is too unstable for us right now and we don't want to complicate our lives any more than they already are. Unfortunately my wife is getting close to the high risk age for pregnancy complications so we're kind of like WTF do we do.....
Right now we're a "wait and see how things go over the next several months" type attitude.