As if it were not confounding enough to watch Ronald Reagan in cozy conversation with communist leader Mikhail Gorbachev, Washington is simultaneously challenged to contemplate the possibility of a harmonious Democratic Party. The world is indeed turning upside down.

For at least as long as Ronald Reagan thought of the Soviet Union as the "Evil Empire,'' reporters have been able to think of the Democrats as the "Quarrelsome Kingdom.'' Some of us even had our word processors programmed to type the phrase ''Democratic disarray'' with a single keystroke.

Before the summit drove the politicians briefly underground, the last sounds heard were loud insults among prominent Republicans. Their intramural crudities contrasted with the dulcet voices of sweet reason from the Democratic choir.

The Republican right was in full cry against its old hero, Reagan, for agreeing to an arms deal with Russia. Confronted with a treaty that polls say two-thirds of the American voters are inclined to approve, many conservative activists could do nothing but howl in protest. One of them, the Conservative Caucus' Howard Phillips, called Reagan ''a useful idiot for Soviet propaganda,'' and another, direct-mail fund-raiser Richard Viguerie, called him an ''apologist for Gorbachev.''

Four of the six Republican presidential candidates joined a batch of Republican senators in denouncing Reagan's handiwork and/or his rhetoric. Remarkable as this outburst on the right was, it paled in wonder to the sudden outbreak of harmony among the Democrats. In last week's NBC television debate, all six of their presidential candidates chirped endorsements of the Reagan-Gorbachev treaty and cheerily minimized any disagreements among themselves on any other aspects of foreign policy.

Now anyone over the age of 8 knew the Democrats' good behavior could not last. Indeed, as soon as the NBC debate shifted to domestic issues, the Democratic candidates were happily snapping verbal towels off each other's backsides, making sure the sting could be felt.

Knowing of that primal instinct for self-annihilation, Democratic National Committee Chairman Paul G. Kirk Jr. has bravely declared the 1988 party platform off limits for intraparty ideological warfare. At a summit of his own last week, he assembled the Democratic leaders of the House and the Senate and the chairman of the Democratic governors to endorse his proposal that the platform be kept short, sweet and noncontroversial.

Instead of another 45,000-word document like the 1984 platform, with ''a line here or a word there . . . to satisfy every disparate group in our diverse society,'' Kirk recommended the Democrats write a brief ''open letter'' to the American people, simple and bland enough so no Democratic candidate anywhere would need to repudiate it and no Republican would find it profitable to attack.

Stay away from ''narrow-interest'' issues like abortion, Kirk suggested -- thereby bringing down the wrath of activist Democratic women's groups. Emphasize such safe promises as ''change'' and ''confidence'' and ''pragmatism'' and, oh yes, ''national teamwork.''

It's almost too easy to parody this as a plea for pabulum. But Kirk, a former Ted Kennedy lieutenant, genuinely has come to believe that the less the Democrats say as a party on the issues, the better chanceDemocratic candidates have to win. He called off the scheduled 1986 midterm policy conference, where liberal party activists were prepared to update the 1984 manifesto.

He found ample justification for his policy of enforced silence in the success Democratic Senate candidates enjoyed last November in conservative states from the Deep South to the Dakotas. Freed of the burden of explaining their party's stance on any issues, they returned the Senate to Democratic control -- and set about writing liberal legislation and blocking conservative appointees.

Kirk would never acknowledge it, but, in fact, he's asking his party to take a lesson from Reagan. Reagan for years played the rhetorical game with Russia; indeed, even when he lost the nomination fight to President Ford at the 1976 convention, he salvaged what he thought was a partial victory by gaining platform language repudiating the policy of de'tente.

But as president, Reagan discovered that when he gave up the pleasure of pronouncing broad moral judgments about the wickedness of the Soviet system, he was able to enlist the Russians' cooperation in accomplishing some of his foreign policy goals. It is that preference for concrete accomplishment that outrages the ideologues of the Republican right.

Now Kirk is challenging the activists of the Democratic left to weigh the relative importance of winning back the White House or writing their favorite planks into the platform. The howls of outrage will be as loud as those Reagan has been hearing, but in the end, as with Reagan, the promise of practical achievement may prevail.