The DoD is completely different from anything else. You sign a contract and swear an oath. We are mandated to vaccinate for things like flu and covid because we can get a notice to deploy and have less than 72 hours to respond and be on a plane going somewhere. You can also file for a waiver on whatever grounds you can come up with if you so choose to, and it might become not a requirement anyway, and I know people who have. Firefighters and Police and other first responders are city/county employees for the most part. I'm federal. You cannot equate the two.
You certainly shouldn't have caused the loss of employment for people who, as you note, are NEEDED simply because they didn't want to get the vaccine. That is authoritarian government, and you support it.