Ed Martin leaked grand jury material, dropped charges against his own former client, and dressed up like Inspector Gadget to intimidate the New York Attorney General, but he still couldn't make it out of the first round.
If an attorney chooses to publicly air controversial opinions, they can expect to get fired. Law firms are a business first, and if their public-facing professionals make statements that alienate clients or create the whiff of a hostile work environment, the firm can cut ties to protect its business. It's not a free speech thing, it's just business. That said, firing someone over their remarks is always a question of "coulda and shoulda."