If your website is a corporation hitting all the legal prerequisites for fairness requirements (size, market share,...), then yes, you must accept my neo Nazi comment. You are allowed to make rules that ban views on other grounds than its content, such as being spammy or off topic to the conversation, but you would have to have objective and neutral criteria for those bans, and you should be obligated to justify yourself to your users with non-automated means, and the banned users should be able to sue you at little or no cost if they perceive unfairness.

The local Christian cake shop are not a corporation and, by the very definition of 'local', almost certainly doesn't meet the legal prerequisites for fairness regulations, so they should not be forced to bake a cake against their will.