Insisting that your employees get vaccinated makes a lot of sense on a "keeping the workplace healthy" basis. A vaccinated workforce makes it less likely that key personnel will be sidelined (or die) as a result of an easily avoided serious illness.
First, let's put to rest the notion that a vaccine mandate is a violation of personal autonomy. A vaccine mandate is exactly the same as saying you can't work for this company if you have a four-letter obscenity tattooed on your forehead.
I mean, you can go ahead and get that tattoo. That's your right. But you can't expect an employer to tolerate it, even though that tattoo is far less harmful to the other employees then being unvaccinated.
Anti-vaxxers, regardless of their political affiliation (and they come from both the right and the left) are obviously incapable of differentiating between science and nonsense, incapable of identifying logical fallacies, and just plain lacking in common sense.
Those intellectual shortcomings make it highly unlikely that the individual in question will make good decisions, if those decisions require the ability to analyze data and follow a logical argument.
That's especially true in engineering, manufacturing, marketing, and sales. If somebody lacks the common sense to be vaccinated, how can that person be expected to make common-sense decisions when it comes to product features or customer relations?
I might add that the same is true of employees who believe off-the-wall conspiracy theories. I had to fire my accountant after he told me that the Apollo landings were fake. How could I trust his advice if he was that gullible?
A vaccine mandate is an easy, legal litmus test that identifies those individuals in your organization who are not capable of thinking clearly. Thus, if they leave because they won't be vaccinated, it increases your company's organizational intelligence.
You're better off without them.