I'm arguing about whether we can control who draws the line about what beliefs are acceptable enough for someone to be employable if we decide it's okay in any circumstance.
Businesses decide on their own company values, and they usually center around being a respectful, honest, hard working employee that fosters an environment that will be good for that particular business. I'd wager most business owners only care about providing for their families, and their employees; about growth and a decent future for what they work every day to build as their very own. Occasionally you get some crackpot religious fanatic owning a bakery or something, who doesn't want to serve people because they're gay or have too much melanin. You can bet your bottom dollar those prejudices are already influencing their hiring practices - but those businesses will never become a multi million or billion dollar franchise, because they're exclusive, prejudiced and doomed to be as small in profits as the owners are small in mind.
Successful, inclusive businesses, where rational people would want to work - have every right to protect their image, and protect themselves from the absolutely bad-for-business associative poison that is having neo-nazi white supremacists in their ranks.
These people deserve the unemployment line, they deserve to be socially ostracized, they deserve to be forgotten when they finally pass from this world, flushed, down the toilet of history - devoid of all achievement, nameless, remembered only for the fact that society bettered them and progressed in spite of them.