THE AFL-CIO HAS DECIDED to have it out with President Carter, publicly and with the volume turned all the way up The crucial early weeks of the new administration have left the federation bruised and aggrieved. It helped elect Mr. Carter and now, it charges, he won't honor his debts. Lane Kirkland, the AFL-CIO's secretary-treasurer, delivered an itemized indictment in an address here the other day.

First there was the choice of the Cabinet - with, Mr. Kirkland feels, a disproportionate representation for big busineee. Then there was the Carter program for economic recovery and its $15 billion a year in tax cuts and spending: the AFL-CIO thought that it should have been twice as big. Next came the President'd rejection of the $3-an-hour minimum wage. On top of all that, there was the President's decision last week not to put tarriffs and quotas on imported shoes.

That's an interesting list, and it shows you pretty clearly where the trouble lies. It starts with two very different views of inflation. Mr. Carter thinks that inflation deeply frightens peopls, and that the country can't get the unemployment rate down when the inflation rate is rising. The AFL-CIO takes the traditional position that a president's first duty is to create jobs right now, by whatever means necessary, and worry about inflation later.

The federation emphatically joins Mr. Carter in oppsition to wage and price controls. But it wants him to go much farther and abandon any attempt whatever to police the inflation rate. It objects to prenotification of wage and price increases. It wants him to rescind the Ford administration's rule requiring inflationary impact statements. It even wants him to abolish the Council on Wage and Price Stability. It wants to get rid of all these things because it believes that they get in the way of creating jobs. But Mr. Carter's economists keep telling him that inflation destroys jobs. It's not the kind of difference that you can easily compromise.

Mr. Kirkland was angry. He devoted three-quarters of his speech to a denunciation of the president's shoe decision and, in general, the encroachments of foreign trade. For a good many years the AFL-CIO has been adamantly and fiercely protectionist, but it's never put the case more explicitly. The administration argues (correctly) that imports hold down prices for American consumers. Mr. Kirkland replied by deriding "the cult of the consumer."

It's quite true that shoe imports threaten American jobs - but those aren't the only jobs that deserve consideration here. Cutting imports would hurt sales in the shops. One competent estimate suggests that for every three jobs that tariffs and quotas could save in American shoe factories, there would be two jobs lost in the retail stores. It's a small example of a larger truth. If you take oil out of this country's foreign trade figures, you will see that the United States exports more goods - particularly machinery, aircraft and foodstuffs - than it imports. All of those exports represent jobs in this country. The federation has locked itself into a doctrine that would protect one job at the expense of another.

In this predominantly white-collar society, it's mainly been the unions that have upheld the broad interests of the people who work with their hands and do the production jobs. That social advocacy has been indispensable to the internal balance of this country. But now the federation keeps getting itself hung up in narrow quarrels that pit one kind of working people against another. It seems to be losing its natural allies, including its former friend in the White House. That's a greater cause for concern, in our view, than the statistics on imported shoes.