Church-state skirmishes in sight?

Last week's Republican election landslide raised sweeping church-state issues: * Ronald Reagan, the Republican platform, and Sen. Orrin Hatch (R) of Utah, new chairman of the Senate Labor and Human Resources Committee, favor tuition tax credits to students at private schools and colleges. This involves federal aid to parochial schools. The election would appear to give the movement a boost.

* Five times Congress has failed to pass a constitutional amendment overturning the Supreme Court's ruling in 1962 and 1963 against prayer and Bible-reading in public schools. Both Mr. Reagan and the GOP platform favor school prayers, and Sen. Jesse Helms (R) of North Carolina is seeking to end court jurisdiction over state laws dealing with "voluntary prayers in public schools."

* Newly coordinated evangelical action groups, long featured on television and symbolized by the Rev. Jerry Falwell's Moral Majority, urge a stronger political role for fundamentalist views.

* The Republican platform backs an anti-abortion constitutional amendment and the appointment of anti- abortion judges. The new Senate Judiciary Committee chairman, Strom Thurmond (R) of South Carolina, does not go all the way on this, but Senator Hatch, who will head the judiciary subcommittee on the Constitution, backs the anti-abortion amendment.

In terms of specific legislation, the long-debated tuition tax credit measure , which would affect 12 million students, of whom 4 million are at parochial schools, is of the most immediate moment.

The House passed a bill on this matter in 1978, but it failed in the Senate. The bipartisan measure is sponsored by senators Bob Packwood (R) of Oregon and Daniel Patrick Moynihan (D) of New York. Strong opposition on "separation of church and state" arguments beat the bill in 1978. Now it comes up shortly in the new Congress, and sponsors declare it has a much-increased chance of passage in the changed political climate.

The Republican platform attacks Democrats on the issue, noting that "wielding the threat of his veto, Mr. Carter led the fight against Republican attempts to make tuition tax credits a reality."

By contrast, President-elect Reagan wrote in his book, "Call to Action" in 1976 that "thousands of parochial and private schools close down because they can't compete with public schools, which drain off more and more in taxes."

Election returns show a substantial shift of Roman Catholics from the Democratic Party to the Republican. Reagan got 48 percent of the Catholic vote compared with Carter's 40 percent. This reverses the old New Deal coalition pattern.

"For the first time in US history," wrote Leonard DeFiore, parochial school head here, to all Roman Catholic bishops during the election, "a major candidate for the presidency [Reagan] has specifically voiced views on major issues which are so precisely compatible with values and interests of great importance to the Catholic community."

He continued: "Specifically, I am referring to Governor Reagan's deep convictions about the right to life of the unborn, about traditional family values, and about tuition tax credits for parents of private and parochial school students."

Presidential candidates often fuzz issues after elections, a practice that critics charged to Carter. In his press conference in Los Angeles Nov. 6, Reagan was asked his attitude to conservative religious groups that supported him.

He would be president of "all the people," he answered, and would seek advice from those "familiar with a particular problem."

"In other words," he said, "I am not going to separate myself from the people who elected us and sent us there."