The TUITION tax-credit bill, reported last week by the Senate Finance Committee, threatens to do incalculable damage to this country's public schools. It would provide huge tax subsidies to private and religious elementary and secondary schools, without restriction. It promises a multibillion-dollar bonanza to schools serving every kind of ethnic and social separatism -- by race, by class, by national background. These credits would, for the first time in the nation's history, swing enough tax money into the private schools to change fundamentally the balance between them and the public schools. Heedlessly and irresponsibly, the Finance Committee has voted out a bill that would erode one of the central institutions of American life.

Who's responsible? It started with Sen. William V. Roth (R-Del.) and his bill to give a $250 tax credit for college tuition. The idea had a lot of appeal in Congress. The lawmakers have belatedly begun to sense the wave of resentment from their middle-income constituents, on whom they have loaded a disproportionate share of the current increases in the Social Security tax. The tuition credit seemed like a nice way to tell the middle classes that their friends in Congress haven't altogether forgotten them.

It was a bum bill, but it didn't touch any basic principles. The American tradition in college education has been pluralistic from the beginning. Federal aid goes, in great quantities, to public and private colleges alike. By the time students reach college age, they are inevitably going in many diverse directions, and there is a public interest in helping them along. The question is how to do it, and the Roth bill was objectionable merely because it would have wasted a lot of money.

But the Finance committee's tax credit is altogether another matter. Sen. Daniel Patrick Moynihan (D-N.Y.), with the assistance of Sen. Bob Packwood (R-Ore.), devised language extending the credit by 1980 to the elementary and secondary schools -- and doubling it. On Thursday the expanded version whipped through the committee, 14 votes to 1, under the always efficient chairmanship of Sen. Russell Long (D-La.). It was a piously bipartisan assault.

American law and usage have always treated schools differently from colleges. Most Americans understand that it takes a strong sense of national community to hold this huge and heterogeneous country together. That sense of community arises, above all, from the public schools -- the experience that a child shares with others of widely differing backgrounds and conditions for 12 years or so while growing up. Subsidies that encourage parents to take their children out of public schools will inevitably diminish this strength.

We shall doubtless hear from people who argue that it is unfair to make them pay through taxes for public schools and then pay again through tuition for a private one. We disagree. If parents use a private school, that is a voluntary choice. But if they get tax subsidies for it, then it is other taxpayers who have to pay twice. They have to pay once for the public schools and again through the subsidy for the private one -- and that is involuntary. If you don't like swimming in the neighborhood pool, that's up to you. But don't ask the federal government to help pay for the private pool that you want to build in your back yard.

The Finance Committee would give parents a tax credit of half the tuition they pay, up to $1,000. That's $500, and a tax credit is the same thing as a cash grant. The subsidy is big enough to start a rapid growth of every kind of private school. The Carter administration points out that by contrast, federal aid to public schools comes only to $128 per pupil. The administration adamantly opposes the whole idea of this credit, and so will anyone else who values the public schools.