Officially, inside, the capital city was going about its usual mimeographed, well-rehearsed business: David A. Stockman testifying on the budget, Sen. Alan Cranston (D-Calif.) announcing his presidential peace candidacy, angry citizens protesting the certification of El Salvador.

Actually, outside, the city was trying to prove that it has lost its mind. It was wearing feathers, war paint, oversize Styrofoam mittens with elongated index fingers proclaiming "We're No. 1", carrying banners that said "R-E-S-P-E-C-T." They seemed to be saying that Washington, for all its reputation as a swampland breeding gray bureaucrats and bad ideas, is really a place of passion, willing to undergo any hardship and make any sacrifice for what it believes in, which happens to be a football team.

Some detached observers felt that the downpour, which attended the joyous orgy of the Redskins welcome, might have represented God's opinion that Redskin fever should subside.

But the heavy rain was to the fans a challenge, an opportunity to show the world that they care beyond considerations of reason and health about one team of men who shoved another team of men up and down a field in Pasadena last Sunday night--and made Washington a city, and life worth living for everybody in it.

The hooting, horn-blowing, trashing frenzy that immediately followed their victory was something that might have occasioned stern denunciation for other demonstrating groups, like peace marchers for instance. Smashed car hoods and tops--they became walkways to the celebrants--were tolerated by the police, who also winked at drinking in the streets.

The public happiness was so enormous that heretics who smirked during the football strike were reduced to cowardly silence. Some even defensively watched the game for fear of the opprobrium that would be decanted on any who willfully stood apart from so cosmic, and bonding, an event.

All week long, shopping mall amplifiers played "Hail to the Redskins" the last line of which is "fight for old D.C." Old was suddenly an endearment for the city that politicians love to hate.

The day that President Reagan sent his indefensible budget to Congress, the same day that he offered to meet Soviet leader Yuri V. Andropov "anywhere, anytime," he journeyed to Dulles, put on a funny burgundy-and-gold cap and told the victorious coach, "You have brought the city together."

Reagan was so carried away that he admitted government workers, whom he last acknowledged by proposing to freeze their pay, to membership in the human race. He gave them two hours leave to watch the Redskins "parade," which turned out to be a courtesy term for what ensued.

Experts, including the players, have sought to explain why Washington was transformed by a few touchdowns that occurred a continent away. Joe Theismann, the Redskins quarterback, said it was "an escape from some of the harsh realities." For some, this raises the question of what could be a harsher reality than being thrown to the ground by some well-paid bruiser from the other side and carted off the field on a stretcher.

But apparently what Washington the city likes about football is what Washington the government earnestly strives to eradicate from society. Sexism (it's all-male), elitism (season ticket-holders occupy almost all seats at Redskins games) and violence (see above) can be cheered in the stadium.

The fever raged, and not without its militant, even menacing moments and its big hype. A woman driving up Connecticut Avenue during the Tuesday night rush hour, came upon a group of drunken fans in a traffic island, waving a banner that said, "Honk If You Like Hogs." She didn't, and they moved in on her car in a manner she found so alarming she honked. Local TV announced inaugural-scale preparations: live coverage, seven camera platforms. They exhorted Washington to beat Miami again by turning out more than the 100,000 who greeted the drubbed Dolphins. They did.

The streets leading to the flag-decked District Building presented the sight of people possessed. A young woman, her hair plastered to her forehead, held a thoroughly sodden infant in her arms. An elderly man with a cane hobbled painfully through the rain. Two impeccably tailored middle-aged women stood dripping on a corner emitting hog calls in honor of the offensive line of the Redskins, who were supposedly passing by in a bus all but obscured by a sea of umbrellas.

"You yell now, Grace," said one to the other. "I can't do any more."

Up the street, dozens of demented fans stood on the hoods and roofs of four police cars. One roof had begun to cave. What would have happened to peace demonstrators who tried the same thing hardly bears thinking about. It was the day's most dramatic proof that, to paraphrase Barry Goldwater, extremism in praise of professional football is no vice, even in Washington.