The Washington Teachers' Union, which less than a year ago helped defeat Douglas E. Moore in his campaign for City Council chairman, asserted its political independence from Mayor Marion Barry yesterday and endorse Moore for City Council at large member in the May 1 special election.

"This is a new election and it doesn't follow that we simply go the way of all flesh," union president William H. Simons said. "Simply because the mayor has selected a candidate (lawyer John Ray, Moore's principal opponent), does not mean we are in the mayor's hip pocket."

Moore strategists heralded the endorsement as an indication that the diverse collection of special interest groups that makes up a significant portion of Barry's political base would not be atomatically delivered to Ray, despite Barry's active campaigning on Ray's behalf.

"It still amazes me that people believe in a coattail theory. In this city, it hasn't worked," said Moore's son, Douglas Jr., who is running his father's campaign.

But Ray, who has maintained that not all of his votes will come from Barry regulars, noted two other unions that had endorsed Barry-those representing the city's firemen and police-have yet to endorse Moore. Moore's strategists have been counting on that support.

Ray added, "When the teachers cast their votes, I'm gonna have more than Doug."

About 5,000 of the city's 6,200 public school teachers are members of the union. Simons said the union, which is facing $343,350 in court fines stemming from an illegal strike last month, had little financially to contribute to Moore's campaign.

But, Simons said, the teachers would provide poll watchers for Moore all day long at each of the city's 137 voting places. Simons said the effectiveness of the union during the strike should be an indication of how well it will be able to work for Moore's campaign.

During the strike, Moore marched alongside the striking teachers, and described them as "second-class citizens." He said yesterday he favors increased funding for the city's public education system.

Neither the firemen's union, Local 36 of the International Association of Firefighters, nor the police union, Local 442 of the International Brotherhood of Police Officers, has voted endorsements yet, union officials said yesterday.

The teachers' union also yesterday endorsed retired government management analyst and former teacher Dorothy M. Maultsby for City Council in Ward 4. The teacher endorsement is considered important there because it is one of two city wards where a large number of teachers live. The other is Ward 5.

"They never will have to wonder if they go out again," Moore said of the teachers. "They will have one person (on the council), Douglas Moore, who will stand with them and not hide and duck."

Last year, when Moore ran against Arrington Dixon for council chairman in the critical Democratic primary, the teachers' union endorsed Dixon. Simons would not elaborate yesterday on the union's sudden preference for Moore, except to say, "You're talking about two different sets of circumstances."

Moore, repeating a refrain that has become a major theme of his effort to win a political comeback in the May 1 election, declared, "This is a new day for a new mission for a new people in Washington, D.C."

The one-time political maverick also said, "We no longer have to look at limited visions in this city. People have tried to box me into a certain position, to not permit me to move into the mainstream of D.C. politics."

The "people," he said, referred to the news media, and especially The Washington Post. Moore said he has not really changed his politics, even though he once declared that this campaign would see a "new Doug Moore."

There was a whole list of things (I did) which for some reason, people have not looked at. At this point, people are really beginning to look at what Douglas Moore has done for the economic growth and development of the city," Moore said.

It is these selected past deeds that Moore has been touting on the campaign trail. Moore's new style of delivery, an adviser once proclaimed, is a return to the "Professor Moore" image he cultivated during his first successful campaign in 1974.

"Why should you vote for Douglas Moore?" was his Socratic-like opening line at a Southeast Neighbors candidate forum last week in the Hillcrest area of the city.

Moore frequently has been accused by political opponents of being an unproductive member of the council while he served from 1975 to 1978. During that time, he also had several scrapes with the law that some felt represented unacceptable behavior for a public official in a city just returned to long-sought and limited home rule.

Last year, Moore ran his council chairman campaign with heavy attacks on the city's business community in general and the Metropolitan Washington Board of Trade in particular. He also crusaded against gay rights, legalized gambling and decriminalized marijuana. Moore lost convincingly to Dixon in the Democratic primary.

The "new" Moore, as the 50-year-old Methodist minister and former Black United Front chairman has called himself, is going around the city pitching hard on what he calls a "solid record of legislative achievement."

Part of that record is the introduction of 64 pieces of legislation, including, Moore says, the first two city budget bills submitted and approved by the home rule council. Moore also portrays himself as a veteran of community struggles, such as a campaign against bus fare increases.

"Douglas Moore has a track record," he told a candidates' forum audience recently at Shiloh Baptist Church. "That's why you know the name. The rest you do not know because they have done absolutely nothing but come before you for office.

"What is their goal?" he said of his 10 opponents. "What have they done? Where are they going? Nowhere."

Moore says his legislation included a measure tacked on to the council's budget bill last year which limits the amount of increase in property taxes from one year to the next, regardless of rising assessments.

Moore also was the first member of the council, he says, to propose guidelines for the city to deposit its money in District banks rather than the U.S. Treasury. (The bill finally enacted was sponsored by two other council members). Moore's guidelines were designed to discourage redlining and to steer some deposits toward minority-owned financial institutions.

That showed not only his concern over segregated housing and for minority banks, Moore says, but also won him points with city bankers, who have a chance to hold some of the deposits.

Moore also is reminding businessmen that it was he who last year supported an increase in the city's mortgage loan ceiling to 11 percent, rather than the politically more popular 10 percent limit.

Moore is quick to trumpet his proposal to limit condominium conversions in the city and, during a time of increasing utility costs, remind his audiences that he once sponsored legislation to eliminate the fuel adjustment charges on some utility bills.

The other candidates besides Ray in the at-large race are David G. Harris, Lin Covington, Richard Blanks Sr., Frannie Goldman, Warren A. Hemphill Sr., Hector Rodriguez, H. Chris Brown, Jackson R. Champion and Stuart D. Rosenblatt. CAPTION: Picture, Washington Teachers' Union President William Simons announces union endorsement of Dorothy M. Maultsby, left, and Douglas E. Moore, right. By James A. Parcell-The Washington Post