Bar owner George Watson’s politically incorrect humor at the Dock Bar & Grill in Montauk has seemingly caught up with him.Posted on the window next to the entrance of the local mainstay, a list bars “Irish Drunks” from patronizing the establishment—along with “yapping mutts,” “screaming kids,” cellphones, strollers and those who only want to use the restroom.It was the “No Irish Drunks” that upset Pauline Turley, the vice chairwoman of the board of the Irish Arts Center in Manhattan.In an email on Tuesday morning, Ms. Turley said she had visited the bar in April and had a nice time over a pint of Guinness and mussels. It wasn’t until she was leaving that she noticed the sign and was taken aback.“I raised an eyebrow and wondered how many other ethnicities would allow an ethnic slur on a window, took a picture, and went about my weekend,” she said.It wasn’t until an Irish news website, IrishCentral, posted a story about an equally eyebrow-raising sign in a pub in Ireland—it read “No Loud Americans”—that she decided to share her photos of the sign in Montauk.“I sent it to them, curious how their readers would feel about it,” she said. “I do often think that it is because of our self-deprecating attitude that such drunken stereotypes are allowed to prevail. Ireland, like many countries, has its fair share of dealing with issues related to alcohol. Binge drinking is a serious issue for our youth. And I’m not sure our ability to laugh it off is helping the situation.”Since the photos she took of the sign and the story went up on the internet, the Dock and Mr. Watson have been receiving a deluge of criticism. On the Dock’s webpage, users berated the bar.“Such insensitivity and racist remarks should not and cannot be tolerated,” said one commenter, Greg Seán Canning. “As an Irish man and as the Florida State President of the Ancient Order of Hibernians, I take personal offense to this sign, which was displayed on your glass window. Shame on your establishment for allowing this to take place.”John Cunniff took a more caustic view: “No Irish drunks? I guess Italian drunks are okay, or German drunks, or Russian drunks. Just not Irish ones. Thanks for reminding me of why I moved away from Long Island. Tool.”Mr. Watson has also taken flak on the telephone while working. “Once this hit the papers, the phones were ringing off the hook. One guy calls up and says, ‘Listen, you can’t be doing this. Don’t be picking on the Irish. You gotta pick on the ...’” Mr. Watson said, rattling off a long list of different racial slurs the man had used. “I explained [to another person that] the joke wasn’t meant to hurt anybody. It was an inside joke taken out of context. He wouldn’t let it go, so I said, ‘Say ... three Hail Marys and you’ll wake up with a sense of humor.’”Mr. Watson, who is of Irish descent and acted as grand marshal of the Montauk St. Patrick’s Day Parade in 2003, said the sign was inspired by being “worn out of patience” while running the bar. He said there are certain things he can’t handle, like people bringing a double-wide stroller into the bar when it is packed, or when people tie their dogs out front and the dogs won’t stop barking.“A bunch of customers who were Irish, at least a dozen of them, had gone over to Block Island, and they got off the boat totally shit-faced and came in and were literally screaming at me for two hours. That is why I put that sign up,” he said, noting that it has been on display for nearly five years. “I’m not allowed to serve drunks. I would make that distinction—I don’t care whether you’re white, black, yellow or pink.”Since the backlash, he’s placed a piece of paper with the word “sensitive” over “Irish,” so it now reads “No Sensitive Drunks.”Ms. Turley said his fix was a “clever retort,” but Mr. Watson said he plans to permanently replace the paper with “sensitive”—in “Kelly green.”Mr. Watson is a former Fire Department of New York firefighter and has owned the bar since 1973. On the Dock’s website, he writes: “At The Dock, we feel that in order for a joke to be funny, it must be told at someone’s expense. We tell ethnic, sexist and racial jokes—everyone gets their turn in the barrel.”Each day, the Dock’s chalkboard features a joke, a poke at someone, or a silly inward reflection. This week, messages scrawled in chalk included “A firm purpose of amendment: I’m sorry, I apologize, I went to confession. It won’t happen again,” and a checked-off “Bucket list update: Piss off ancestral homeland.”Mr. Watson said he writes a newsletter called “The Truth,” where he is always making fun of people. “I don’t complain about any payback,” he added.He said people are too sensitive.“I think 98 percent of people get the joke,” he said about the “No Irish” rule. “It’s wackos that are offended by it.”