If their values are "we cannot interact in a professional manner with people who hold views we dislike," their values are bad and they should compromise them. If we can't get along with those with whom we disagree when necessary to accomplish unrelated things, we might as well disband this country and start arming up for civil war, because that's where this road ends.
Maybe you could. Maybe, if someone had consistently argued that you and your family were of an inferior race and should bow to their will as is your ordained place in the universe, you could shrug it off and say, "let's agree to disagree and get on with things".
I'd guess this has never happened to you though. I'd guess you can have this position because this is not your safety and your rights that are in danger. It's always so much easier to consider hatred acceptable when you're not its target.
In a professional environment we all have to compromise. You can't expect to only run into people who share your values and/or validate and approve your life style, or even what you feel is your identity.
I'm fine with working with people whose don't share my values. I wouldn't be with someone who very publicly and very repeatedly advocated me and my family being enslaved. If you are, good for you! just don't expect everybody to share your obvious strength of character and forgiving nature.