All over town yesterday, everyone close to the consumer movement, inside and outside the government, could talk of nothing else - the Ralph Nader-Joan Claybrook falling out.

People in Nader's offices said they could do absolutely no work yesterday, having spent the day on the phone answering questions about the split. Not one of them said they had known anything in advance of Nader's decision to call for Claybrook's resignation as head of the National Highway Traffic Safety Administration because he felt she had been a failure at the job.

At the National Consumers League reception at the Central Hilton last night, honoring Washington Post political cartoonist Herblock for his efforts on behalf of the consumer movement, both the friends-turned-adversaries showed up and the definitely were the nights topic of consideration.

Claybrook, once Nader's chief congressional lobbyist, had little to say on the subject, though she admitted her agency, which had "enjoyed a quiet period" before she came, "is in turmoil now."

Asked if she were still speaking to Nader, Claybrook said she had no comment. "My feeling is the isue has been exposed." Then she put her finger to her closed lips, shook her head, smiled and walked away.

But everyone else, including Nader, had plenty to say. Not only is he still speaking to Claybrook, who was once his very best friend but "If she's willing to come back to the citizen movement," she said, "we'd love to have her."

A lot of people at the recognition felt that was the real reason Nader had asked for her resignation, and not because she supported a delay on mandatory air bags for automobiles. Nader said last night Claybrook would be better for society on the outside than as a bureaucratic puppet." He insisted than his was not a personal attack, simply "an attack on her performance," but he agreed that it had been a "very difficult thing to do."

Others said it was "like a lovers' quarrel. A lot of emotion came through in that letter," one woman said, referring to the 11-page typewritten Nader called for Claybrook's resignation.

"I'm afraid this is going to split the consumer movement," a mutual friend of their said. "People are going to take sides and it's easy to side with Joan." Nader acknowleged that she 'would get the sympathy vote," but he said. "I'm fighting her battle and getting the flack for it. If I lose a friend because of this, she's not a friend." Those who work with nader took great pains to explain why he criticized his best friend. "Ralph is more interested in saving lives than in keeping friends. To him it's a matter of life and death."

"Isn't it fascinating," said one corporate lobbyist, hardly concealing his glee.