On Monday, Walt Disney Co. Chief Executive Bob Chapek said he didn’t want to wade into politics. He finished the week pledging to crusade against anti-LGBTQ legislation across the country and in a public fight with the governor of the state that houses his company’s most famous asset.

Mr. Chapek on Friday took the most drastic step yet in trying to quell anger over Disney’s response to a Florida bill known by opponents as the “Don’t Say Gay” bill, saying the company was pausing all political giving in the state and boosting efforts to fight similar legislation in other parts of the country.