THE REAGAN administration's tuition tax credit bill is in trouble. The problem is this: the administration has sent up a bill that provides tuition tax credits of up to $500 for parents who send their children to private schools. (Yes, that's a tax credit, not a deduction--an extremely generous way to encourage private schools and one which, in the case of religious schools, we think clearly violates the First Amendment ban on government support of religion.) But the administration bill does not provide for enforcement by the Internal Revenue Service, the government agency directly involved, of the ban on credits for tuition to schools that discriminate on the basis of race.

That has troubled some senators who strongly back tuition tax credits, such as Sens. Bill Bradley (D-N.J.) and Daniel Patrick Moynihan (D-N.Y.). Sen. Bradley has proposed an amendment, which seems to have majority support on the Finance Committee, to give the IRS enforcement authority. But Bob Baldwin, a lobbyist representing several groups on the religious right, opposes this as a "killer amendment," and says Christian school groups "are not going to give the IRS or any other government bureaucracy an iron boot that allows them to tramp over schools and parents."

The "iron boot" he is talking about is the authority the IRS had by virtue of congressional legislation and a regulation passed in the Nixon administration denying tax exemptions for Jim Crow schools. That was settled policy, widely accepted across the nation, until Jan. 8 of this year, when President Reagan, acting at the behest of supporters of institutions such as Bob Jones University, rescinded the regulation. After the furor (which almost anyone but the administration officials responsible might have predicted) did in fact break out, the president publicly regretted his action and asked Congress to overturn it.

There is, of course, no good reason why the government, through tax exemptions or tax credits, should subsidize segregated schools. If some groups on the religious right prefer no tuition tax credits at all to a tuition tax credit proposal that does not aid segregated schools, that tells us just about everything we need to know about their priorities: they care more about promoting segregation than about helping private schools generally. Such motives stand in vivid contrast to those, for example, of many members of the Catholic hierarchy, who have worked hard to make sure that their schools do not serve as all-white havens for parents who wish to avoid school integration.

The Reagan administration now has to choose which it wants more: a tuition tax credit bill or an endorsement of segregated private schools. A bill without an IRS enforcement provision is certain to be defeated in Congress; a bill with such a provision has some chance of passage. Does the administration genuinely support the tuition tax credit idea? Or has it just embraced this proposal to win political points with two disparate groups--Catholics and others who run integrated private schools and those who want to promote racial segregation--whose interests are suddenly in conflict? We shall see when the administration responds to Sen. Bradley's amendment.