There's a huge difference between a private institution requiring its employees to get a shot, and the government requiring all citizens to.
Your place of employment has many rules and regulations that you must follow...dress codes, behavior, clock in/out policy, what have you. There's nothing wrong with a company requiring you to get a vaccine, and I'm saying this as an opponent of the vaccine itself. I will not be taking the vaccine, but I don't work somewhere that requires it either.
When the government starts forcing this on ordinary citizens, then we'll talk.