About 12 years ago, the late Clarence Mitchell, then one of the rare black lobbyists working the Capitol Hill corridors of power, came to testify at a civil rights hearing chaired by an old-style southern senator.

Mitchell, representing the NAACP, was scheduled to appear early, but the senator found one reason after another to slip white witnesses in ahead of Mitchell: This witness had to make a plane; another had to go back to the office. After two or three hours, Mitchell, angry but determined to keep calm, was allowed to appear -- last.

For decades, that was a way of life for black lobbyists on Capitol Hill. They were few, they usually focused on civil rights issues, and they often faced insensitivity, humiliation and barriers.

Today this is changing, and Robert M. (Bob) McGlotten is evidence of the change. At 48, he has just become the first black named to one of the most influential lobbying jobs in the nation, representing millions of people -- most of them white.

McGlotten is the new director of the legislative department of the AFL-CIO, which despite membership losses in recent years remains the most powerful social welfare lobbying force in the country. The American Federation of Labor and Congress of Industrial Organizations has 13.6 million members, numerous political action committees run by itself or its 99 international unions, and large numbers of volunteer political workers.

Civil rights, an area in which McGlotten has a lot of experience, is an important part of his legislative assignment on Capitol Hill. But he is also a labor man down to his bones, working on an array of issues that he believes affect all workers, white and black:

International trade problems and the threat they represent to American jobs. The effect of tax revision on low- and middle-income workers. Budget allocations for public services. Improvement of the minimum wage. Strengthening the bargaining rights of unions and the prevention of what the AFL-CIO sees as legislative union-busting. Protection of Social Security, unemployment insurance and Medicare benefits. Improvement of pensions, workplace health and safety, job training.

McGlotten was raised in an Italian neighborhood of South Philadelphia that had only a sprinkling of blacks. His father was a teacher in Delaware and then a chef in Philadelphia. McGlotten attended the public schools and then St. Joseph's College, studying industrial relations, and the University of Pennsylvania, studying law. He has a law degree but has never practiced.

His first job was as an industrial relations trainee in the Philadelphia subway and bus system. Later he worked for the Philadelphia transportation workers Local 234; for the AFL-CIO Council of Philadelphia as an organizer for the Sulfite, Pulp and Paper Workers and the American Federation of Teachers; and for the Rev. Leon Sullivan, a black leader and organizer of job programs for minorities.

In the late 1960s McGlotten spent three years in the national AFL-CIO civil rights department here, working to get minority participants into building trades jobs, then spent two years at the AFL-CIO's Human Resources Development Institute working on job training and affirmative action programs. Next came a spell as special assistant to Labor Secretary Peter J. Brennan. He joined the AFL-CIO legislative department in 1974.

As director of the legislation department, McGlotten has seven AFL-CIO lobbyists working directly under him, plus the assistance of various AFL-CIO departments specializing in subjects such as Social Security. He also can seek the help of lobbyists from constituent unions and other labor groups. Every Monday when Congress is in session, McGlotten meets with about 60 lobbyists from 25 to 30 affiliated unions to exchange information and discuss strategy.

For 12 years, he has been a presence on Capitol Hill, huddling with Senate Majority Leader Robert J. Dole (R-Kan.), Democratic leaders Sen. Robert C. Byrd (D-W.Va.) and Rep. James C. Wright Jr. (D-Tex.), and a host of others of both parties on the major bills.

McGlotten lobbied heavily for a trade protection bill that was passed by the House over presidential opposition in May. "The biggest issue for labor now is trade -- the question of fairness," he said in a recent interview. "We want to protect our markets from unfair trade practices, whether it's dumping by others or not allowing us to export goods to other countries." Labor believes, he said, that the administration is not doing enough to combat practices by other countries that are wiping out millions of American manufacturing jobs.

Tax revision is another major issue for the AFL-CIO, and while the organization does not endorse all provisions of either the House bill or the Senate committee bill, it supports both versions generally, in part because they would "lower the burden of taxes on low-income and middle-income people, close loopholes and shelters that have no economic significance in the real world." And the AFL-CIO strongly opposed taxing workers on the value of premiums for health insurance and pension contributions paid by their employers. "We won on that," McGlotten said.

As Congress begins to focus on the 1987 budget, the AFL-CIO is striving for more money for grants to communities for basic services, and to hold the line on funding of basic federal programs. "After all, they don't have to gut the occupational safety and health laws to kill them -- just cut funds and there's nobody to administer them," McGlotten said.

The AFL-CIO is one of the most powerful groups in the Save Our Security (SOS) coalition of more than 100 organizations opposed to cuts in Social Security and Medicare, and in the Health Security Action Council. "There are shifting coalitions on other matters -- it depends on the issue," McGlotten said.

He said his activities and the political action committees that make contributions to candidates are only "a small part" of labor's political clout. "The important part is that our members are willing to participate in politics at the grass-roots level. Our members talk to the members at home. We're able to really mobilize in almost every congressional district in the country."

The AFL-CIO is also a major participant in the Leadership Conference on Civil Rights, a coalition of 185 labor, black, senior-citizen, women's, church, disability and social action groups that spearhead civil rights action.

But McGlotten noted the change in recent years that has seen black lobbyists move into areas other than civil rights. "The number of blacks in lobbying jobs has increased since I first started in 1974," he said. "Blacks are a part of society and most politicians understand that. Institutions are picking their best lobbyists to represent them, and if they're black, they're black."

McGlotten quickly listed lobbyists and legislative analysts who are black and are working not for civil rights groups but for labor and business organizations on general legislation: Gene Casraiss, United Auto Workers; Calvin Johnson, AFL-CIO; Kimberly Parker and Mike Reid, American Postal Workers Union; Peggy Bracy Brown, American Federation of State, County and Municipal Employees; Earl C. Robinson, International Association of Machinists; Dave Claxton, United Food and Commercial Workers; Stacey Mobley, du Pont; Wendell Holloway, Ford (now on leave to run for Congress); Freddie Lucas, General Motors.

"In my years of lobbying, I've never known a member to shut the door because I was black," said McGlotten. "This is 1986, and we're talking about issues that affect all workers, black and white. Society has changed."

McGlotten does not assert that the world of 1986 is completely without dislike or prejudice, because "the general attitudes out in the public apply in the Congress, and you instinctively know if someone has an attitude" against blacks. "But as far as closing the door, I haven't found it.

"In fact, there's more hostility in some quarters because you're from labor than because you're black.