With respect, if the concern is violence at the picket line, essentially the answer offered here is to ban the replacement worker to alleviate the conflict at the picket line. Honestly, fundamentally, it is no better, morally or legally, than saying, “Ban the picket line.”
Essentially, if the issue is managing tensions at a picket line, you are taking an enormous stick to deal with an issue that is serious but not catastrophic across the country. It seems like the wrong fix if that's the problem.