Within the fraternity of professional public opinion pollsters, Rep. John B. Anderson's independent presidential campaign is regarded today as a serious challenge that could result in Anderson's election to the White House next November.

Though there are some dissents from this view, many of the country's best known pollsters said in recent interviews that Anderson has an extradordinary opportunity to do well next fall at the expense of President Carter and Ronald Reagan.

Even those most enthusiastic about Anderson chances agreed, however, that today's visible support for him is based on vague public impressions of him and strong distaste for his two rivals. Unless Anderson can develop strong, positive support for his candidacy and positions, he will quickly become a minor candidate, the pollsters agreed.

All of the pollsters questioned said that Anderson's position is fragile. For more than a month, almost every poll taken in the country has given Anderson 19 to 25 percent of the vote, but none of the pollsters regarded that as solid Anderson support.

Instead, they generally agreed, those relatively high numbers for an independent candidate revealed a high level of discontent with the likely Democratic and Republican nominees and an unprecedented willingness by a large number of people to entertain voting for an independent.

"There is a vast amount of instability in the electorate," said Daniel Yankelovich, preisent of the firm of Yankelovich, Skelly & White in New York. He attributed that instability to a combination of discontent with the choice between Reagan and Carter, and a widespread feeling that the country is in deep trouble.

"Right now," Yankelovich said, "the Anderson candidacy is the obvious place" for discontented voters to go. Whether that remains true is problematical, he said.

Added Louis Harris, whose polls for ABC News have shown strong national support for Anderson, "Any one of the three [Anderson, Carter or Reagan] could win it clearly" in November.

Mervin Field, who conducts the well-known California Poll, which has also shown strong backing for Anderson, compared the Illinois congressman's position to a law of physics. Matter can either rise up under its own power, or it can be sucked up by a vacuum, Field said. In Anderson's case it's the vacuum that elevated him. "There's no question that Anderson is up there because he's not Ronald Reagan or Jimmy Carter," Field said.

Popular knowledge of Anderson in superficial, Field added. Favorable attitudes toward him could be "reinforced or demolished by events," he speculated.

Robert Teeter, a pollster who works for Republican office-seekers, was one of the most skeptical about Anderson's prospects. (Teeter worked for George Bush in this year's Republican primaries.)

"I'm about 80 percent convinced that Anderson is going to end up a minor candidate," Teeter said. "But he's a tinderbox, and if someone should drop a match on him . . ." Teeter did not finish the sentence.

Teeter, Field and several others pointed to a dilemma facing Anderson. He now enjoys the support of a generally liberal, prosperous, well-educated group that Teeter called "the Volvo crowd" or "the trendies."

"The trendies have signed on," Teeter said, "but the group he needs is much bigger" -- working-class Americans -- "and it will get turned off if he starts to sound like a figurehead for the trendies."

Field made the same point, saying it had been unfortunate for Anderson to be filmed in California last week talking about gay rights to a crowd that included a large number of homosexuals.

"All he needs is for that kind of footage to be shown around the country just as people are poised to make a decision about Anderson," Field said, and the independent's candidacy could wither. Like Sen. George McGovern (D-S.D.) in 1972, Field suggested, Anderson will be judged by the company he keeps, and many ordinary Americans will reject him if he appears to be the candidate of flaky fringe groups.

Dr. George Gallup, the elder statesman of American psephologists, noted that traditionally, one-third to one-half of the voters who express support for a third-party candidate before election day end up choosing the Democrat or Republican in the voting booth. This factor contributed to his own wrong prediction about the outcome of the 1948 election, Gallup recalled ruefully, because so many Henry Wallace supporters switched to Harry Truman on election day.

Nevertheless, Gallup joined nearly a dozen of his colleagues in agreeing that 1980 is not likely to be a year for traditional voter behavior. Gallup is intrigued by a recent Gallup Poll showing that if offered the chance to choose between the Republicans, Democrats and a new "Center" Party identified only as "middle-of-the-road," 31 percent of registered voters picked the new party. Of the rest, 36 percent chose the Democrats, 20 percent the Republicans and 13 had no opinion.

Gallup said Anderson's best course might be to cultivate those who wanted a "Center Party," hoping to build such a grouping into a winning force in the future even if he cannot win the 1980.

The pollsters interviewed generally disagreed with the conventional wisdom that Anderson is bound to hurt Carter more than Reagan in November. Field thought this was true, but Gallup disagreed, and Harris and Yankelovich disagreed sharply.

"Anderson's going to hurt the weaker candidate," Yankelovich said. "That's Carter now, but it may not last." As matters now stand, he added, a supporter of Carter or Reagan who sours on his candidate between now and election day will find it easier to turn to Anderson than to the other major party candidate.