Marcia addressed your points very well.
I have one additional question.
Suppose you run a company that builds websites. You are known in the industry and you have an established brand. When people see you websites, they say, "wow, that must be a Lutz Scheffler website".
Suppose a group comes along whose actions you detest. It could be a supremacist group or some other group that practices discrimination.
They want you to build a website for them. You refuse, stating that you don't want your brand associated with their practices.
Should you be subject to civil and even criminal penalties for refusing to accommodate them?