TROY, MICH. -- Struggles for control of the Republican Party apparatus here and in South Carolina are revealing fissures in President Reagan's majority coalition of 1980 and 1984, splits that carry potential liabilities for the party and its leading candidate, George Bush.

In both states, the fights have spilled over into the courts, producing the kind of divisive litigation that leaves scars on the party, in some ways more characteristic of the rules-dominated Democratic Party of the 1970s than the GOP of the 1980s.

As if this were not enough for a Republican Party seeking to convert itself into a permanent majority coalition, both intraparty contests have pitted the party establishment against a Christian insurgency, precisely the kind of conflict party leaders have been seeking to avoid for the past eight years.

These two states have become battlegrounds for different reasons: South Carolina because this year the party organizes itself in a series of county conventions, giving televangelist Marion G. (Pat) Robertson a chance to test his southern political machinery; Michigan because it will be the first state in the nation to pick delegates to the 1988 convention, in an arcane process that began last August.

The central pattern -- a conflict between Bush forces and Christians intent on gaining a piece of power in the GOP -- is likely to be replicated through much of the South and in such states as Minnesota and Iowa.

The contest for control of the Michigan Republican Party has already become a demonstration of the fragility of Bush's presidential bid, raising questions about the legitimacy of the claim of Bush campaign manager Lee Atwater that support for the vice president in the state is "a mile wide and a mile deep."

The state Republican Party has been taken over by an "Anybody But Bush" coalition of supporters of Pat Robertson and Rep. Jack Kemp (R-N.Y.). If Bush is to meet his own goals of winning a majority of delegates from Michigan, his backers must regain power in the state GOP, which effectively controls delegate selection.

The fight has taken its toll on Bush loyalists. "Politics is a game for grown men," Peter Secchia, the state's national committeeman and a Bush backer, said. "When it isn't fun anymore, they should get out. I'm not having a hell of a lot of fun."

More importantly, however, the fight has produced the kind of hostility that makes restoration of a unified party in the general election much tougher to achieve.

In South Carolina, William DePass, an official of the Richland County GOP, demonstrated the extent of this hostility by characterizing a gathering of Robertson forces as similar to "a Nazi meeting." In Michigan, Secchia, a millionaire lumber dealer, showed equal antipathy, describing the state party, now taken over by Christian and conservative activists, as looking "like the bar scene from Star Wars."

Robertson backers, in turn, have delighted in crushing the GOP establishment -- often identified with Bush -- in counties as diverse as Charleston, S.C., and Macomb, Michigan.

While the Michigan contest has revealed weaknesses in the Bush campaign -- he faces a tough, expensive fight attempting to win a state in 1988 that he carried by a 2-to-1 margin over Reagan eight years earlier -- it has also raised doubts about the strength of another candidate seeking to claim the Reagan mantle: Jack Kemp.

In setting up the machinery for the selection of national convention delegates, Michigan officials devised a system that in many ways was ideal for the kind of conservative insurgency planned by Kemp's supporters.

The key election was held in the August 1986 primary, when some 9,000 Michigan precinct officials were chosen. This is the kind of low-turnout, low-visibility contest that lends itself to domination by a determined group of activists such as those forming the core of the Kemp campaign.

In fact, however, Kemp loyalists running for these precinct positions came in a distant third, winning about 10 to 15 percent of the contests, compared with success rates exceeding 40 percent for both Robertson and Bush. Clark Durant, Kemp's chief organizer here, has been reduced to the claim that "the key game has not been to get Michigan delegates. It's been to challenge people to talk about the future."

In South Carolina, there is little of political substance at stake, except an attempt by Robertson forces to show that Bush forces can be embarrassed in campaign manager Atwater's home state. Here in Michigan, however, if the delegate selection process were held now (instead of next January, when it is to be held), there is no question that Bush would be decisively beaten.

In last February's gatherings of the precinct delegates, the Kemp and Robertson forces played hardball, adopting winner-take-all strategies when they held just slim majorities. Bush forces, in contrast, permitted proportional representation of Kemp and Robertson backers in some districts where Bush had a majority. The result has been that for now at least the anti-Bush alliance controls two-thirds of the party.

A word of caution: while these struggles will be difficult for the GOP and its future nominee, they won't have the same effect as similar conflicts have in the Democratic party -- conflicts between such constituencies as blacks, working-class whites, advocates of women's rights and white southerners. In those Democratic factional struggles, the Republicans offered a palatable alternative to some of the feuding groups, such as southern whites. In the Republicans' current troubles, the danger is more that losers in the primaries will sit out the general elections than that they will go over to the Democrats.The writer is a member of The Post's national staff. ". . . the fight has produced the kind of hostility that makes restoration of a unified. . . party much tougher."