Reaction in the administration yesterday to the collapse of West German Chancellor Helmut Schmidt's coalition government ranged from a widespread view that the West may be losing one of its most respected leaders to a feeling that a new, conservative Bonn government would be more politically in tune with the Reagan White House.

Specialists in the White House, State and Defense departments cautioned that it is not clear how the political situation in Bonn will work out. But with the end of Schmidt's eight-year rule apparently in sight, officials offered some early assessments of how a change in leadership might affect U.S.-West German relations.

A predominant view among the European specialists here is that, despite the arrogance for which he is well known, Schmidt is among the world's most respected and important statesmen.

Despite Schmidt's differences with recent American administrations on some issues, his stature as a leader has been a plus for the western alliance and U.S. interests, in this view, especially because there is no one of similar position in the wings.

On the other hand, some more conservative members of the administration, while not disputing Schmidt's stature as a leader, believe that the political values and ideology of a new conservative government of Christian Democrats and the Christian Social Union sister party are potentially more important to the Reagan White House.

"Let's face it, the SPD are not our best buddies," one official said of Schmidt's Social Democrats. "The CDU," he said of the Christian Democrats, "are our kind of guys."

One White House insider noted that President Reagan has "a great deal of respect" for CSU leader Franz Josef Strauss, in particular, and that Reagan went out of his way to meet with Christian Democratic leader Helmut Kohl here and in Germany.

Another specialist said, however, that while the West German conservative parties are always more vocal about protecting the special relationship with the United States, Bonn under Schmidt has followed middle-of-the-road foreign policies that have had conservative support.

This specialist said he believes that, while a new conservative government may be a little tougher than Schmidt on relations with the Soviet bloc, Bonn's options for change are limited.

The departure of Schmidt from the chancellery also could affect two issues, missiles and a gas pipeline, in the Bonn-Washington relationship.

Schmidt has been a staunch supporter of the NATO plan to station new American missiles in Europe beginning in 1983, which officials here are already beginning to call "the year of the missile" in recognition of the political controversy surrounding the deployment.

Schmidt has been able to control the left wing of his party, which opposes the deployment, while retaining the conservatives' backing. With Schmidt and the Social Democrats out of power, the opposition to the missiles will be larger and more vocal, specialists agreed.

The political upheaval in Bonn could have several effects on the Reagan administration's controversial efforts to block construction of a Soviet-West European natural gas pipeline, the specialists said.

Initially, with Bonn distracted by domestic political concerns, one of the effects could be a slowdown in discussions in the alliance on how to heal the breach between Washington and its allies supporting the project. Without Schmidt, a strong and articulate advocate of going ahead with the pipeline, the general European position could be weakened.

Some Pentagon officials think a conservative government in Bonn might be more amenable to future economic pressures against Moscow, but State Department officials are skeptical of that