The first interagency clash over the new Reagan approaches on regulations and civil rights may develop between the Department of Labor and the Equal Employment Opportunity Commission.

The issue is a proposed withdrawal by Labor's Office of Federal Contract Compliance of a rule that would prohibit federal contractors from paying membership fees for any of their employes to organizations "which discriminate in membership on the basis of race, color, religion, sex, or national orgin," according to a notice in the March 27 Federal Register (page 19004).

The Carter Labor Department pushed the rule through and published it on Jan. 16, four days before President Reagan took office. It was scheduled to become effective Feb. 17.

That effective date was delayed by the new president's executive order freezing all pending regulations. In the interim, the Reagan Labor Department conducted "a full review of the deferred regulation" and found that the payment of such dues to an organization that may discriminate "is not itself a violation" of the federal order that prohibits employment discrimination by federal contractors.

"Indeed," the department found, "the regulation of such payments may raise serious legal problems."

But before the Reagan Labor Department could publish its notice proposing withdrawal of the rule, it had to get a waiver from EEOC, an agency that supported the regulation. EEOC, which has a long, militant record of pushing for new antidiscrimination actions, granted the waiver. But it made it clear, according to the notice, that the waiver "does not constitute a change in EEOC's views or original concurrence on the underlying regulation."

Of course, the Reagan administration has not named a new chairman for the EEOC, so this may be the actions of a headless agency, operating on past momentum.