It's a peculiar situation. In most countries the vocal minority opposed to vaccines and other public health measures is just that - a minority. But in the US, some states have a majority that vehemently oppose these measures, and have surging cases and hospitalizations, while other states like in New England have vaccination rates comparable to the best in the world. Not sure such a patchwork of philosophy and culture is so manifest anywhere else and will be interesting to see if the surge spills over into well protected areas. As such, there is no real firewall between them, I'm not aware of any restrictions across state lines.
There is talk in the US in some states of making the vaccine mandatory for healthcare workers. Actually it’s already happening. As the push to end this pandemic strengthens, you may see more private companies creating policy that enforce vaccination. There is no restrictions across state lines that I’m aware of either.