What are those consequences?
Many have still not been defined, as the COVID-vaccine era is just emerging. But as others have pointed out, some airlines (a.k.a. private companies) are already choosing not to offer service to unvaccinated customers. I can foresee many other private businesses doing the same. There is no doubt that nearly all public schools will require it for employees soon (many already do, more in the works all the time), and once there are vaccines available for children, those will be required, too (same as many vaccines already are required for enrollment today). Eventually, most universities will require it for enrollment as well. I'm sure that many health care companies require it of their employees, too, as most already do for flu or hepatitis.
So yes, you can choose not to get a vaccine, but you will be opting out of air travel, public education, college education, opportunity to work in health care, etc, etc. And yet, as isolated as they will be, I know that millions of luddites will still choose to (literally) die on this hill. Good riddance.