Evangelical Christians, spurred by the prospective presidential candidacy of television evangelist Marion G. (Pat) Robertson, are flexing their political muscles against Republican Party regulars in states as diverse as Michigan, Iowa, New Mexico and Tennessee.

Robertson's success this week in recruiting precinct delegate candidates in the first round of Michigan's long and complicated presidential nominating system -- upstaging efforts by Vice President Bush and Rep. Jack Kemp (R-N.Y.) -- is the clearest demonstration so far of the growing influence of the Christian movement.

The breadth of Robertson's political appeal has yet to be tested, and questions remain over whether any television evangelist can reach beyond a narrow slice of the electorate. But at least in some pockets of the country, evangelical voters have emerged as key players in Republican Party politics:

*In Indiana, which has boasted one of the strongest Republican organizations in the nation, Christian-backed candidates decisively defeated party-endorsed candidates in two congressional primaries this month. In one, Don Lynch, assistant pastor of the Independent Nazarene Church, won the Republican nomination without a headquarters and with only $4,000 in campaign funds.

*In Iowa, a key state in the presidential nomination process, evangelical Christians have taken over the party apparatus in Des Moines and in nearby counties. The drive was coordinated by Steven Scheffler, Iowa director of Robertson's Freedom Council, who has achieved the status of a party boss. "It's just at the beginning," boasts Dudley Rutherford, pastor of the Exciting West Side Church. "It's just the tip of the iceberg."

*In the congressional district that includes Chattanooga, Tenn., many business leaders and GOP regulars, including Labor Secretary William E. Brock, are supporting John Davis in his bid to oust Rep. Marilyn Lloyd (D-Tenn.). Davis, however, may not get the chance. Church of God member Jim Golden is trying to mobilize Christian voters to defeat Davis in the Republican primary.

In many respects, the Republican Party is an ideal target for evangelical Christians. Polls indicate that white, born-again Christians represent about 20 percent of the total electorate and have moved overwhelmingly toward the Republican Party.

Because of party rules, a small but highly motivated group of activists can exercise significant influence. In Michigan, for example, the winner of the Aug. 5 primary could be the candidate whose organization persuaded 3,000 to 4,000 people to run for Republican precinct delegate. This means that mobilizing just 0.1 percent of the electorate could translate into a victory in the first test of prospective Republican presidential candidates.

Similarly, in states such as Iowa and Minnesota, the GOP precinct caucus system means that any group equipped to turn out five to 50 people in a majority of precincts can take over the party structure for an entire congressional district.

In some cases, the Christian mobilization has run into problems. In Minnesota, a bitter disagreement over tactics has split the influential Christian-Republican movement, sharply reducing the chances that the Christian-backed gubernatorial candidate, Mike Menning, can win the party endorsement.

Robertson has encouraged much of the Christian political activity. Defying the rule of thumb that prospective presidential candidates should avoid taking sides in primary contests, he has been endorsing candidates and helping them raise money.

In Indiana, this strategy paid off for Robertson, who received some of the credit when state Sen. James Butcher upset state Treasurer Julian Ridlen for the Republican nomination in the 5th Congressional District.

Robertson hosted an early fundraiser for Butcher that produced $35,000, representing more than 20 percent of Butcher's primary campaign war chest.

He has raised similar amounts for Golden in Tennessee and for Paul Becht, who is given an outside chance of winning the New Mexico Republican gubernatorial nomination.

Not all of Robertson's gambles have paid off. He supported Kent R. Hance's unsuccessful bid to win the Texas gubernatorial primary, and in California, the Robertson-backed candidate, Mike Antonovich, in running third in polls for the Republican nomination for Senate.

In terms of presidential politics, the most important developments have been in Michigan and Iowa.

In Iowa's Polk County, the largest and most influential in the state, and in neighboring Dallas County, the moderate-conservative wing of the Republican Party was overwhelmed by an outpouring of Christians in precinct caucuses. In this new world of religious politics, traditional ward organizations are being replaced by such churches as the First Assembly of God and First Federated, each of which produced more than 50 of the delegates attending Iowa's 4th District Republican convention.

At the county conventions, Christian organizers passed out papers headlined: "How to Participate in a Political Party." Among the guidelines: "To a degree, keep your position on issues to yourself . . . . Come across as being interested in economic issues . . . . Hide your strength . . . . Don't flaunt your Christianity, this is predominantly friendship evangelicism."

The power of the Iowa Christian movement was most apparent when Mary Louise Smith, chairman from 1974 to 1978 of the Republican National Committee -- the highest national party office -- was barely elected from her precinct to be a delegate to the Polk County convention. The six people attending the precinct caucus split 3 to 3 for five ballots, until finally the conservative-Christian faction gave in and allowed her to go to the convention.

In an interview later, Smith said: "They [the Christian conservatives] have as much right to be there as I have -- that's the process. It's the exclusionary part of the process that I object to. It's almost a kind of unreasonable imposition of their views on the system -- moral and religious views on the political system -- and a lack of willingness to discuss these issues on the floor, just shutting others out."

In Indiana, John Sweezy, chairman of the powerful Marion County Republican organization, said after his candidate lost to Lynch in the 2nd District congressional fight: "If their intent is to drag or push the Republican Party so far to the right that we lose the center, then they are dooming themselves to failure, because they will lose the election. Our party is a centrist party."

Republican strategists generally agree that evangelical and fundamentalist Christians are a key element of the GOP coalition, and are critical to the long-range Republican goal of gaining majority status. Many, however, fear that divisive battles over such controversial questions as abortion, pornography regulations and tax credits to religious schools could harm the party.

For the moment, Democrats are delighted with the victories of evangelical Christian candidates in Republican primaries. The Democratic Congressional Campaign Committee has compiled lists of Christian-backed candidates, along with extensive news clips about them, on the theory that many of the fundamentalists make poor general election candidates.

This assessment proved inaccurate in Minnesota in 1984, when the GOP took over the state House of Representatives, breaking what had been a Democratic hammerlock on the legislature. Since then, however, Christian squabbling within the Minnesota GOP appears likely to set back the movement and its candidates.

For Robertson, the blossoming of evangelical political power has given new impetus to his possible presidential bid. He now asserts that "I've been urged by tens of thousands of cheering people around the country to be the champion of traditional moral values . . . . I'm looking at what the evangelicals do in Michigan. I think it's very important. It's one thing to stand up and cheer and say, 'We want you.' It's something else to say, 'We are going to get out in the precincts.' "