The furor over the firing of Bella Abzue, one of the nation's most flamboyant feminists, is symbolic of the problems President Carter has faced in attempting to grapple with women's issues, difficulties that likely will haunt him within the Democratic Party in election year 1980.

The firing, a bizarre drama played out in a series of White House meetings Friday, was only the latest in a series of Carter confrontations over women's issues that began before his presidential nomination.

Ironically, it comes only a month after the party, with White House approval, moved to require that half the delegates to its 1980 convention be women. This ensured that activist women, already a potent force in the party, will be even more powerful when Carter seeks renomination.

With this group, decidedly more liberal tnan either Carter or the party as a whole, conflict is almost inevitable. "Any administration that tries to be moderate on women's issues is bound to confront difficulties in this day and age -- both from the fright and the left," complained one administration official yesterday.

But more was involved in the fight with Abzug than narrowly defined "women's issues." The OMEN'S ADVISORY COMMITTEE WHICH SHE HEADED HAD ATTACKED Carter for his budgetary policies -- hikes in military spending and cuts in social programs.

These are the same conflicts that have put him at odds with liberals in his own party. And in a sense the fight with Abzug is reflective of that broader fight.

Carter's relationship with the more militant elements of the women's movement and other liberals has always been tenuous. He wasn't the first choice of many of them in 1976, and his aides worked strenuously to moderate party platform language on abortion and homosexual rights.

Carter, one strategist said, was sympathetic with the general aims of the women's movement, but sensed a "problem of style and taste" with it that alienated much of the country. He wanted to avoid the "radical" label that fell to Sen. George McGovern, the 1972 Democratic nominee, and balance the broad goals of the women's groups with political realities.

During the 1976 platform committee meetings and at the convention, Carter's aides went along with the general liveral thrust of the platform. But they worked to tone down "buzzword" language favored by some women's groups.

One of his key supploters in the convention was Midge Costanza, then vice mayor of Rochester, N.Y., and cochairman of Carter's New York campaign. As a reward, she was given a job as the president's highest ranking female assistant and an office just down the hall from his.

Former representative Abzug was credited as a moderating force among the more militant women at the convention, and went away thinking Carter was in her debt. "Bella certainly could have made things more difficult for us," one adviser said at the time.

Last June, Abzug was named cochairwoman of the National Advisory Committee for Women, an unsalaried job.

Now Costanza and Abzug, both extremely independent and outspoken, are gone from the administration, stripped of their duties in messy episodes that drew protest from women's groups.

Both were declared guilty of not being team players.

Abzug was fired after a controversial press release fell into Shite House hands. The release, prepared on Thursday for use after a meeting Abzug's group had scheduled with Carter Friday, criticized Carter's proposed cutbacks in social welfare programs and increased in military spending.

These aren't what many would consider women's issues. But aside from that there were incications that Abzug had attempted to undercut Sarah Weddington, the president's new adviser on women's issues.

Costanza resigned last August after being moved to the Shite House basement and eased out of many of her duties.

Carter has had other problems with women's groups.

When he first entered the White House they were angry that he hadn't picked more women for top posts, although two members of his Cabinet were women -- Commerce Secretary Juanita Kreps and Housing and Urban Development Secretary Patricia Harris.

Later there were complaints about his stand on abortion. He opposes federal financial aid to indigent women seeking abortions, although he refuses to support a constitutional amendment outlawing legalized abortions.

There were complaints last fall that the administration was slow to mount a strong effort to extend the time permitted for approval of the Equal Rights Amendment.

The ERA ratification extension was eventually passed with White House approval. Symbolically, Carter's mention of this was the only line that drew loud applause in the president's address to the Democrats' midterm convention in Memphis last month.