OF COURSE, President Reagan is not a bigot. No one has meant to imply, in all those questions about the civil rights record of his administration, that he is in the same category as Senator Bilbo, or even Archie Bunker. He is believed when he says, as he did at Wednesday night's press conference, that he was "raised in a household where the only intolerance . . . taught was intolerance of bigotry." Everyone knows that he had black friends on the football team at Eureka College and that he was genuinely moved by the story of Barbara and Phillip Butler, whose Prince George's County home was the scene of a cross burning.

The difficulty is that, while good will and freedom from prejudice may be enough to expect from an average citizen, it is not enough to expect from Ronald Reagan. A president is responsible for more than his own personal conduct. He is called upon to enforce the laws, defend the constitution and lead in the formulation of the government's policy toward minorities.

It is this public responsibility that has given civil rights leaders cause for concern. They are worried because budgets have been cut for civil rights enforcement efforts. Black Americans were discouraged by his long delay in calling for extension of the Voting Rights Act and then by the Justice Department's opposition to strengthening amendments passed by the House. The final compromise was a good one, and it was gratifying to see Mr. Reagan sign it this week. But the tension and suspicions engendered during the bitter struggle for passage are not immediately dispelled by a stroke of the pen.

Civil rights leaders have been dismayed by the quality of some of the president's nominations to sensitive positions--two had to be withdrawn in the face of widespread opposition. There is also an uneasy feeling among minorities that the qualified and able blacks in the administration do not play an important policy-making role on civil rights issues. Finally and most dramatically, blacks and whites alike were astounded by his decision last January to reverse 12 years of government policy by granting tax-exempt status to schools that segregate. True, the outcry produced some backtracking and a consensus that the Supreme Court should settle the question. But it is easy to see why the initial decision caused such an uproar. The injury was compounded when it became clear that Mr. Reagan and his closest aides had neither anticipated the strength of the reaction nor understood the depth of feeling that produced it.

These are the issues that trouble civil rights leaders--these, and a broader fear about unemployment and about the dismantling of social programs that is not limited to blacks but which affects them in greater proportion. It is not Mr. Reagan's personal convictions or attitudes that are at issue, but the public policies of his administration. And it is on that level that the debate belongs.