>a business may not want to associate with someone who has opinions counter to their own

I'm not sure it's so much that exactly as businesses don't want employees who make a lot of other employees uncomfortable or who hold loud (whether deliberately or because social media made something go viral) opinions or make stupid jokes in public that get associated with the company and cause PR issues.

The fact is that if someone employs/sponsors/advertises with/etc. you they can and will cut ties fast if you embarrass them.