But people are being fined and businesses destroyed because they will not submit.
People are being penalized for breaking the law. Not for what their ideas.
The law targets their ideas for suppression.
Bullshit! The law targets their behavior towards others. They are free to believe whatever they want.
And they're free to refuse service to people they don't like - as long as they keep mum as to their reasons.
You totally misstate the law. A refusal to abide by public-accommodation laws without offering an explanation would result in a finding by a state human-rights agency against the business owner. The complaining party must fill out forms with either the relevant state or federal agency that specifies the basis on which the complainant feels that s/he was discriminated against, in writing on a form. The business might try, in defense, to introduce a neutral rule that it has, but this would require evidence that this rule is universally applied to all patrons, i.e. "no shirt, no shoes, no service," when asked for an explanation. I know from years of experience with EEO cases that, in an employment-related case, the employer accused of discrimination is required, once the accuser makes out a prima facie case in court that precludes summary judgment for the employer, to assert a legitimate, non-discriminatory reason for its actions regarding hiring, discipline, denial of promotion, discharge, etc.. The accuser then may present evidence that the proffered explanation is "pretextual," in other words a lie, and then usually wins. Keeping mum is not a way out of it. It's a guarantee that the respondent will lose.