Initial support for President Reagan's proposed revision of the federal income tax code is giving way to uncertainty about its merits, according to a nationwide Washington Post-ABC News public opinion poll.

The public strongly supports some aspects of the plan, such as doubling the personal exemption for taxpayers and dependents to $2,000 each, but strongly opposes other aspects, such as taxing a portion of workers' fringe benefits.

Relatively few people -- 12 percent -- said they think they will pay less under the modified flat tax sought by the president; three times as many think their taxes will increase.

Two of every three people interviewed said the current tax system should be changed. But only 26 percent endorsed the proposal that Reagan calls "America's tax plan." The great majority, 60 percent, say they have no opinion, and the remainder, 14 percent, oppose it.

Those figures show a sharp decline from surveys taken shortly after May 28, when Reagan described the plan in a televised address. A Gallup poll taken during the following two days, for example, reported 49 percent saying the proposal was "a good idea," 23 percent saying it was not, and 28 percent undecided.

It appears that critics of specific aspects of the plan have succeeded in planting public doubts, despite efforts by Reagan to promote it in visits and speeches around the country.

The Reagan proposal would reduce tax rates for most people and eliminate or reduce many deductions. It would take many low-income wage earners off the tax rolls, but in dollar amounts it would be of most benefit to upper-bracket earners and families.

The Post-ABC News poll, taken June 13 to 22, found people tending to believe that the rich would benefit more than any other group, and that the middle class would benefit least, if at all.

Questions about five provisions found enormous backing for one of them: increasing the current $1,040 personal exemption to $2,000. That was supported by 76 percent of the 1,506 people interviewed and opposed by only 18 percent.

In addition, by almost 2 to 1, or 62 to 33 percent, those interviewed favored a proposal to end the business expense deduction for the cost of sporting events, theater or other entertainment.

But by 80 to 17 percent, those surveyed oppose a tax on part of workers' fringe benefits, such as health insurance. Fifty-three percent said they or someone in their home receives such benefits.

A smaller majority also opposes, 56 to 36 percent, ending the federal deduction for state and local taxes. A majority in every income category did not want such a change, despite Reagan administration statements that only the top one-third of taxpayers benefit from the deduction.

Another change would curtail deductions for mortgage interest on a second home. Only 7 percent said they claimed such a deduction this year. Nevertheless, the survey found a sharp split, with 48 percent favoring, 43 percent opposing curtailment.

To a degree, the survey indicated that people favor or oppose the Reagan revisions according to how they think they would fare. All groups, however, have large numbers with no opinion.

Among the 12 percent who think they would pay less in taxes, 56 percent approve the plan, 4 percent oppose it and 40 percent have no opinion. Among the 37 percent who think their taxes would go up, 10 percent favor the plan, 29 percent oppose it and 61 percent have no opinion. And among the approximately half who think their taxes would stay about the same, 33 percent approve the plan, 7 percent disapprove of it, and 60 percent have no opinion.

The Post-ABC News survey also tried to gauge what the public is looking for most in any changes of the tax system. Which comes first: taxes that are as low as possible, fairness or simplicity? Of the three, 56 percent in the survey chose fairness first, 30 percent opted for low taxes and 12 percent for simplicity.

The poll also asked people which of these statements they tended to agree with more:

"A) Taxing wealthy people at a much higher rate than other people in order to help the poor is only fair."

"B) Taxing wealthy people at a much higher rate is unfair, because it punishes the people who have worked the hardest."

A majority of 51 percent said it is fair to tax the rich at much higher rates, 37 percent said it is unfair, and the rest were unable to choose between the two.

The tendency was for upper-income people to be less supportive of progressivity. But even among those in the highest bracket -- the 10 percent whose households earn $50,000 a year or more -- the principle did not go down to defeat: 45 percent favored it, 45 percent were opposed.

There was a sharp partisan split, however. Among Democrats, 57 percent favored taxing the wealthy at much higher rates and 31 percent were opposed. Among Republicans, 46 percent were in favor, 43 percent opposed.

Just over half the people interviewed said the taxes they pay cause financial hardship for them, and a slightly higher proportion, just under 6 in 10, said they consider the amount they pay too high. Eighty-seven percent said they agreed with the complaint that the government "is wasting too much of the tax money it collects," and 81 percent agreed that "many rich people pay hardly any taxes at all."

In addition, 56 percent in the survey agreed that "the government is spending too much tax money on the military," with 38 percent disagreeing and 6 percent expressing no opinion. The public had the opposite reaction on domestic spending, with 37 percent agreeing and 56 percent disagreeing with the statement, "The government is spending too much tax money on social programs."