I imagine it’d be the same sort of thing that happens all the time when people “discover” that the CD they just bought for their kids is full of swearing, or the DVD is full of nudity-- There’d be an outcry, the relevant company would either back off or not back off, and would either gain or lose customers because of it. The market would, in this case, work itself out.
Proctor and Gamble were accused of having hidden Satanic messages in their logo for decades, and after decades of fighting the rumor they finally gave up and changed the logo. I knew plenty of people in college who refused to order pizza from Domino’s because of the owner’s politics. Obviously there wasn’t a critical mass to drive them out of business, but I don’t know if their politics changed (or if it was all urban legend, for that matter…). Same thing, slightly different reasons.
The politics of the (former) owner of Domino’s, Tom Monaghan, were no urban legend. He’s an extremely conservative, pro-life Catholic and contributed large sums of money accordingly. Similarly, the owners of Chik-Fil-A give large sums to organizations which coincide with their conservative (protestant) Christian worldview, some quite religious, others secular/community oriented.
Then there’s Ben & Jerry’s, a brand that many conservatives eschewed for years, until their buyout by Unilever, or the many companies which are (or were) boycotted for their contributions to Planned Parenthood.
It’s hard to get through a day without hearing someone else say that they’d sooner cut off their feet than set them into a Wal-Mart, and I know a large number of people who do not eat at Denny’s or Cracker Barrel restaurants to this day even though both companies have gone to some lengths to distance themselves from the discrimination issues that plagued both for years.
In all of these cases, consumers educated themselves as to issues which are important to them and have made their shopping choices accordingly. They exercise their right to choose, and no one has had to have the force of law coming down on them to make sure that everyone’s personal issues were catered to by every company in the country. (An absolute impossibility, to be certain.)