A conservative group is launching an advertising campaign Tuesday designed to push back against what it sees as "woke capitalism," spending more than a million dollars on ads targeting the CEOs of Coca-Cola, American Airlines and Nike.

The ads are sharply critical of the CEOs on a range of issues ranging from childhood obesity to allegations of forced labor in China. Organizers say the campaign, which is being mounted by the conservative group Consumers' Research, is designed to change the thinking in corporate boards around the economic and political costs of getting involved in flashpoint issues such as voting rights.

"Increasingly we're seeing companies taking their eye off the ball," said William Hild, the executive director Consumers' Research. "Our focus is always on the consumer. And that's what it should be for these companies as well, but increasingly we're seeing them work to curry favor with woke politicians, rather than focusing on serving their consumers."

The dark money group says it will not disclose who is financing the campaign, saying it respects donors' privacy. Consumers' Research says it will run the ads on CNBC, FOXBusiness, and local stations in the cities where the companies are headquartered. There will also be an online component to the campaign.

Replete with ominous video of the CEOS and casting them very much like opposition candidates in a political campaign, the ads target the company CEOs by name. The ads criticize American Airlines CEO Doug Parker for his high pay at time of layoffs and taxpayer bailouts for the industry. They target Coca Cola CEO James Quincey over obesity in America. And they criticize Nike CEO John Donohoe over allegations of forced labor in China. 

Asked for comment on the new campaign, American Airlines referred CNBC to its statement in April on its involvement in the Texas voting rights dispute. "As a Texas-based business, we must stand up for the rights of our team members and customers who call Texas home, and honor the sacrifices made by generations of Americans to protect and expand the right to vote."

Coca Cola and Nike did not immediately respond to requests for comment.

The decision of whether or not to weigh in on political issues is a fraught one for American CEOs, who generally prefer to avoid fights that could alienate a large chunk of their customer base. In a CEO survey out today, Fortune Magazine's Alan Murray reports that chief executives are split "right down the middle" on the issue.

Fifty percent of those surveyed agreed that "CEOs have a responsibility to speak out on important social and political issues and should continue to do so." But another 50 percent agreed with the statement that "CEOs have recently gotten too involved in commenting on social and political issues and need to pull back."

Writes Murray: "More than 80% agree that "everything possible should be done to make it easy for every citizen to vote." But countering that belief is a strong desire to stay out of the partisan crossfire (and perhaps not be called "woke" by the editors of the Wall Street Journal.)"