West Germany's radical Greens party, whose antinuclear and ecology-minded views have jolted the staid style of politics here, is entering government for the first time after agreeing to form a ruling coalition with the Social Democrats in Hesse, the country's fifth-largest state.

Holger Boerner, the Social Democratic state premier, announced last night that the Greens would assume control of the energy and environmental ministry and a junior post in women's affairs. The pact will break a long political stalemate caused by a divided state legislature.

Conservatives quickly branded the nascent "red-green" ruling coalition a dangerous precedent that could lead to a pacifist and neutralist government in West Germany if it were carried out at the federal level. Gerold Tandler, general secretary of the Christian Social Union, called it a "coalition of horror" and vowed that his party would do all in its power to prevent the Hesse alliance from becoming "a model for Germany."

Johannes Rau, a moderate Social Democrat and the party's candidate for chancellor, repeatedly has disavowed the notion of a political alliance between the Greens and Social Democrats and has insisted that he will strive for an absolute majority in national elections 15 months from now.

Rau and other party centrists contend that the Greens' antinuclear and anti-NATO security policies make them unpalatable as federal coalition partners. Social Democratic officials emphasized that the political conditions in Hesse were unique because only collaboration with the Greens would enable Boerner to establish a majority to pass the state budget.

But political analysts noted that Boerner, like Rau, had vowed in recent years never to form a coalition with the Greens, yet was ultimately forced to do so because of the impasse in the state legislature. A similar dilemma could arise after the 1987 elections if Chancellor Helmut Kohl's center-right coalition fails to retain its majority and the Greens remain in the federal parliament, the Bundestag.

Another "red-green" coalition at the state level may emerge next spring after elections in Lower Saxony, where the Social Democrats are expected to require support from the Greens to oust the Christian Democratic government there.

In West Germany, the making of state coalitions often presages the national experience, and the record of two states governed by "red-green" coalitions could be a significant factor in the looming federal election campaign as Rau launches his attempt to unseat Kohl.

Seeking to appeal to the conservative instincts of many West German voters, Kohl's Christian Democrats are flaunting a vision of West Germany pulling out of the western alliance, removing all nuclear weapons and retreating into a neutralist posture under a Social Democratic government beholden to the Greens for power.

The divisive, even chaotic, nature of the Greens has been exacerbated by a protracted power struggle between pragmatists willing to compromise to achieve some objectives and fundamentalists who believe that their role is to expose foibles and hypocrisy in conventional politics.

The coalition deal in Hesse represents a triumph for the pragmatic faction of the Greens over the anti-party iconoclasts, whose style and tactics appear to have fallen into disfavor with many youthful party members as well as the electorate.

At the national level, the Greens' pragmatists have been gaining strength following disastrous defeats in Saarland and in North Rhine-Westphalia, where an uproar ensued over a party call to decriminalize sex with minors.