Religion, values, etc. I've said nothing about politics as far as I know. It seems your problem is with these bills defining owners and businesses as "individuals". That a far better point than to be saying you're more entitled than people you disagree with to be able to be open about your values.
You're the one who brought up neo-Nazis. These bills came about because some people who work in the wedding industry objected to serving gay peoples who needed cakes or photography for their wedding ceremonies. These people claimed a religious objection to that and so Republicans started pushing these laws as a way to avoid lawsuits, I guess. Another possible fallout for laws such as this is that it could lead to people who work in health care citing religious beliefs as a way to refuse to provide certain services to people.
This has nothing to do with protecting the rights of minorities. It's just the opposite. It's about protecting right-wing Christians. It has nothing to do with helping other people out. This bill in Mississippi started out as basically a clone of the Arizona bill but has gone through a couple of revisions that have made it very vague and so it's hard to determine what exactly the bill would do.