AN APPOINTMENT to any federal regulatory agency gets caught up in a certain amount of partisan politics, if only because federal regulation is a political process, engaging strong emotions and powerful economic interests. But an appointment to the Federal Election Commission is something else again, in terms of political sensitivity, for the obvious reason that what is being regulated is not a transportation system or an industry but the business of politics. President Carter has learned this the hard way since he rejected the suggestions of the congressional GOP leaders, Sen. Howard Baker Jr. and Rep. John J. Rhodes, and nominated a liberal Republican, Samuel D. Zagoria, for a Republican seat on the FEC.

The problem is not that Mr. Carter has suddenly "politicized" the agency. He hasn't; the FEC, because it regulates all federal campaigns, has been inextricably enmeshed in politics from the start. If it were otherwise, if commissioners could be chosen purely for their ability and independence of mind, someone like Mr. Zagoria - who has been a journalist and aide to Sen. Clifford Case (R.N.J.) and is now director of labor management relations for the U.S. Conference of Mayors - might be ideal.

But if you grant that politicians are not likely to be perfectly dispassionate in choosing the overseers of their campaigns, then there is a certain pragmatic logic to maintaining a balance on the commission essentially by standoff. Thus the law calls for a panel of three Democrats and three Republicans, and thus Congress in 1974 allowed its own leaders to choose four of the six commissioners, to limit presidential influence over the regulation of congressional campaigns. Even after the Supreme Court ruled out congressional appointments, President Ford respected the wishes of Hill leaders in making his Democratic nominations to the FEC.

It is that bipartisan understanding, imperfect but serviceable, that Mr. Carter has upset. And he has done so in a particularly partisan and provocative way. After rejecting the two names given him by the GOP leaders, he chose a Republican deemed acceptable by organized labor - the very political force that most alarms the GOP. Yet at the same time he did allow the House Democratic leadership to dictate the nomination for a Democratic FEC seat, and wound up naming John McGarry, the candidate of Speaker Thomas P. O'Neill.

Perhaps the White House is right in maintaining that Mr. Carter had never really promised to respect the wishes of Sen. Baker and Rep. Rhodes. Perhaps the GOP leaders were wrong to submit only two names, instead of five or 10, when Mr. Carter asked for more. No matter. The point is that for whatever reasons - lack of understanding, or cuteness, or a desire to tilt the FEC - the administration has now sorely rankled a large number of Hill Republicans, starting with Sen. Baker, whose good will on more important matters, such as the Panama Canal treaties, may become vital and may now be much harder to gain. The White House has also put Mr. Zagoria and his Republican friends in a nearly impossible position and almost guaranteed that someone - or some presidential interest - will suffer. If there is a learning experience in this for the White House, the lesson is not necessarily that you must never play politics with appointments to the FEC - you can hardly keep politics out of it. The lesson is that you ought to play prudent politics - especially when the imprudent course is so easy to see.