The day after a State of the Union speech in which he openly flirted with women voters, President Reagan showed up in Dorchester, Mass., and hoisted a beer at the Eire Pub, an Irish establishment with a huge sign in front that labeled it twice for all the world to see as a "men's bar." In point of fact it admits women, but the picture of the motorcade arriving at the bar in the Boston Globe, for example, didn't say that.

Three days later, the president (and the vice president, and half the administration, for that matter) graced the 70th anniversary dinner of the Alfalfa Club, a pristinely all-male group of 150 high rollers, each of whom was permitted to bring up to three male guests. The list of men who showed up at the gathering was a veritable Who's Who in Washington. It was, as the newspaper headline put it, a quintessential gathering of the old-boy network--a meeting of men so important, so powerful that you'd think they'd be big enough to share.

But they are not. Instead, they barred the press and women from their annual dinner, both of which are the kinds of moves that give public relations people nightmares. All-male clubs, whether they are social clubs that foster the old-boy network or professional clubs that institutionalize it, simply do not enjoy the wide acceptance they did years ago. They may be symbols of success and arenas for fun in some quarters, but in others they are vestiges of an order that maintained supremacy by keeping blacks and women out.

And they are not, for a president who is having trouble with minorities and women voters, necessarily the best places to hang out on a Saturday night.

Appearances are important, even critical, according to one of the president's own men, Robert A. McConnell, assistant attorney general for legislative affairs. On Dec. 23, he wrote a memo to Kenneth M. Duberstein, assistant to the president for legislative affairs, warning that the 98th Congress will feature "significant activity" on "multiple proposals perceived by their proponents to be pro-women." He went on to say:

"We expect a major effort involving hearings and legislative proposals to develop in Rep. Don Edwards' subcommittee on Civil and Constitutional Rights . . . We feel it reasonable to predict that Edwards will attempt to 'corner' the President much the same way he believes he did on Voting Rights in the 97th Congress. That is, act before the administration can organize its position, to establish interest and concern, propose and report some form of an ERA-like comprehensive legislative package, thus forcing the President to support revolutionary legislation or to explain reservations to a public which perceives the president to be weak on women's issues. Posturing will be critical.

"House Republicans are quite restless," wrote McConnell. "They are concerned that this subject matter could be used to their significant political detriment if Republicans do not move quickly with their own proposal or an Administration initiative."

In his conclusion, he stated that "if the administration has any hope of reversing feminist momentum away from the administration, we must recognize that women's concerns are not generally so parochial as 'women this and women that' but arise from perceptions of the economy, military matters and other major national issues."

One of the issues haunting the president is the perception that he is antiwomen's rights. It does not help his cause to have one of his appointees in the Justice Department describe an "ERA-like comprehensive legislative package" as revolutionary. Nor does it help to have the appointee suggest that posturing, rather than substance, will be critical.

Nevertheless, McConnell is half right. Posturing is one way for a politician to get principles and priorities across and to create favorable or unfavorable perceptions in voters' minds. In his State of the Union address, the president demonstrated a more committed posture on women's economic issues than he has in the past. Women's organizations were cautiously encouraged.

In the care and nurturing of this new interest, his staff people would do him a service by watching how close he gets to such symbols of a closed society as all-male clubs. It may not be bad form for ordinary citizens to join them, but it is not the most brilliant political posturing for a president to honor them.