They may intend to take this all the way to the Supreme Court, and with the court's current composition, there's an excellent chance they win and even get the underlying statute neutered or struck down.
If the executives think it's anything remotely resembling a reasonable use of company assets to fight workplace discrimination laws on constitutional grounds, the board should fire them, and if they don't, the shareholders should fire the board. ATVI is a large publicly traded corporation. It's not Hobby Lobby.
That’s not how this stuff works at all. This is a dispute over the facts, and how much money the facts are worth, and to whom. Someone in California DOJ had a 15 minute meeting with their people and ATVI people and already decided that ATVI is going to face a fine to be paid to its female complainant former employees, the next three years of lawsuit is a ceremony enacting that.
Unless they are picked on for a very successful boycott, it's going to be mostly aversion from current and potential employees, with Google-like staff evaporation but with much lower attractiveness.
Does Activision have backup studios in "developing countries" or other clever plans?