Until the Courts or Congress or the White House settle the issue, most employers are going to find a reason NOT to hire you.
It does NOT matter to them why you are a no-vax.
What does matter is if you get sick, or if you infect someone else while performing your job.
“All future employers are worried about their liability if they hire someone who has not been vaccinated.”
And won’t they have a conundrum when it turns out that the vaxxed employees are the ones dropping like flies?