President Reagan established a genial, jocular tone in his highly publicized ''apology'' to the International Federation of Business and Professional Women this week. In the same vein it may be laughingly asked if he has investigated the possibility of a Democratic mole assigned to infiltrate the White House and cross its wires when women are around. How else to explain a series of episodes seemingly calculated to increase the political gender gap just when the administration is putting its best foot forward on various executive and legislative steps on behalf of equal rights?
First there was the mix-up that canceled a White House tour for hundreds of members of the federation. If those responsible were friends of the President, who needs adversaries? Maybe Mr. Reagan suspects they are Democrats; at any rate , he joked he would shove them out the window if he found them.
Then there was the hasty apology appearance. A Democratic mole could hardly have done worse than whoever advised Mr. Rea-gan to speak to this audience of business and professional women in terms of ''the opposite sex'' and women's ''place,'' not to mention the intended compliment that got most attention: ''I happen to be one who believes if it wasn't for women, us men would still be walking around in skin suits carrying clubs.''
This pleasantry was not taken lightly by the federation's president, who not only called it offensive but went on about White House ''insensitivity'' to working women and ''token appointments'' of women in government.
All this after various women's groups were incensed already because the President omitted women entirely from the high-level Kissinger commission on today's hottest foreign policy topic, Central America.
It's only joking to wonder if a Democrat is covertly pulling the strings to damage Mr. Reagan's image with women voters (and with men who regard equal rights as important to maintain the strength of American ideals). But even if the White House is mole-free, Mr. Reagan does need to get his official household in order on this matter.
After all, when he first breezed into Washington, a long-time congresswoman spoke warmly of meeting him and having confidence in his good intentions even though he and she disagreed on how to pursue equal rights. Somehow these good intentions must not be obscured by displays of administration insensitivity.
If appointing the first woman to the Supreme Court was a token, it was some token! Mr. Reagan also has put three women in important cabinet-level jobs. As an alternative to the Equal Rights Amendment, he has set in motion efforts to identify and eliminate discrimination in federal and state laws.
To be sure, more leadership against discrimination would be welcome. But the substance of the Reagan record should be judged on its merits. The Reagan team needs to help the President avoid any appearance of remaining in the age of caveman jokes.