No A&E isn’t exposed to suit. Guarantee there’s a bad press clause in the contract. And yes they do care what people say on FB, especially when what they’re saying is “we’re boycotting”. They know word of mouth is still the most effective form of advertising ever invented and social media has only made it more effective. ACLU won’t be coming after them. Advertisers don’t like controversy, as soon as this blew up the advertisers started running scared, they know how this goes, boycotts and counter boycotts. They also know how it all blows over, the big thing the advertisers want is for everybody involved to STFU and let it blow over so the ratings don’t get dinged next month.
A&E is exposed to suit from the gay lobby groups, as is any company or association in this country, now that the big outfits have gone over. Even if they win, they can’t because money runs scared. Which is why Aristotle said that a plutocracy is the worst of all forms of government. It has no moral core.