Businesses are supposed to be separate entities from the individuals who own them. I don't understand why people think businesses need to be political. If that's the case then just start your own Political Action Committee.
These are liberal analogs to, e.g., conservative claims about the how Civil Rights Act would directly lead to blacks and latinos raping and murdering whites, or in more recent years similar insinuations (and sometimes outright claims) regarding border controls. When you can draw a straight line between abstract policy preferences and the imminent death of an untold number of people, dissension becomes intolerable. Most people tend to agree with that sentiment on its face--that's why political rhetoric so often regresses to such stark terms--the sticking point is what that line looks like, if it even exists at all.
EDIT: I keep forgetting that the misuse of science is nothing new, so liberals aren't actually bringing anything new to the table in that regard. Of course science (certainly poor science, yet sadly mostly only in hindsight generally recognized as pseudo-science or non-science, e.g. Social Darwinism) was used to justify those example conservative claims, as well countless similarly specious claims from across the political spectrum going as far back as one cares to look, but particularly after empiricism displaced both institutional religion and rationalism as the fount of categorical truths.
Are you sure that wasn't largely a southern Democrat thing? For the Civil Rights Acts of 1957, 1960, and 1964, ~80% of Republicans voted for them. Meanwhile, only ~65% of Democrats voted for them. It was mostly southern Democrats filibustering/voting against the bills.
https://en.wikipedia.org/wiki/Civil_Rights_Act_of_1957 https://en.wikipedia.org/wiki/Civil_Rights_Act_of_1964 https://en.wikipedia.org/wiki/Civil_Rights_Act_of_1960
Before civil rights legislation, the Republicans were the party of capitalism, industry, protectionism, and to an extent urbanism; in the early 20th century they were defined mostly in terms of opposition to progressivism (antitrust, workers rights, regulation) and the New Deal. Democrats were the party of farmers, states rights, and (see previously) progressivism and the New Deal. You can look at this as a "conservative/liberal" split, but it's a different one than we have now.
It was only after the CRA that the process was set in motion to polarize the parties perfectly by conservative/liberal ideology (in the sense we use those terms today). And that process didn't even really finish until around the 1980 election; for example if you look at '70s Republican party platforms, for instance, they're still playing footsie with being pro-choice.
So it just doesn't mean much to rebut someone saying "conservatives opposed the CRA" with "no, the Democrats did". There were essentially 4 parties at the time: the liberal/conservative wings of both parties.
That doesn't really apply when your business is essentially selling your own image and personality.
Just remember that politics isn’t everything.