Washington — President Reagan's plan for federal tax breaks for students in private and parochial schools is one of the most controversial presidential recommendations in years.
His trip to Chicago to tell the National Catholic Educational Association that he wanted to ''expand education opportunities by supporting a tuition tax credit plan that would permit parents to take a credit on their income tax for each child they have in private school'' stirred instant debate.
The Reagan proposal raised certain questions:
* Will Federal aid for private and parochial schools damage tax-supported, non-denominational municipal public schools, currently hard pressed in some communities?
* Can the Treasury afford to lose an estimated $4.6 billion annually by 1987 at a time when substantial deficits are anticipated?
* Does the First Amendment to the Constitution separating church and state permit federal tax aid to schools emphasizing religion?
Mr. Reagan received a cordial reception from his immediate audience as he repeated pledges made in his nomination and election campaigns. He argued that his proposal would aid the American educational system.
''I would like to think,'' he said, ''we are offering help to the inner-city child who faces a world of drugs and crime, the child with special needs, and the families who still believe the Lord's Prayer will do less harm than good in the classroom.''
The comment recalled Supreme Court rulings that religious observance in public schools may violate the First Amendment prohibition of a state-supported church.
The Reagan proposal set off reaction from expected sources.
In support are Sens. Daniel Patrick Moynihan (D) of New York and Bob Packwood (R) of Oregon, who favor a system of tuition tax credits. It failed in Congress in 1978, but is the vehicle for a new drive.
Supporters say that as Roman Catholic families migrate from urban areas, church membership in some districts has fallen off. Tuition alone isn't enough to meet the cost of schooling, and credits or direct payments are needed if the parochial schools are to fulfill their mission of educating minority children.
Frank J. Russo Jr., president of the Catholic League for Religious and Civil Rights, argues that for every pupil who transfers from a public school there would be a net savings in state and local taxes of $1,000 a year.
In opposition, R.G. Puckett, executive director of Americans United for Separation of Church and State, says ''This scheme, designed to pay off political debts, will be disastrous for public education, interfaith harmony, and sound economy.''
Sen. Ernest Hollings (D) of South Carolina argues the plan would undermine public education, aggravate the federal deficit, and violate the Constitution.
Albert Shanker, head of the American Federation of Teachers, said his organization would oppose the proposal in the face of planned cuts in US aid to education.