Since the Justice Department made a grant to a coalition of women's shelters last summer, Phyllis Schlafly says, she has been upset about "giving government money to a feminist group to pursue feminist goals."

Now Schlafly, the self-styled spokeswoman for traditional women and an ardent foe of the Equal Rights Amendment, has evened the score. She helped persuade senior Justice Department officials to award $622,905 to a group of her associates to study the problem of family violence.

The newly formed Task Force on Families in Crisis, which received the grant last month, consists mainly of officers and volunteers from Schlafly's conservative Eagle Forum. Schlafly had urged Assistant Attorney General Lois Haight Herrington, head of the Office of Justice Programs, to approve the grant.

People for the American Way, a liberal lobby, attacked the award yesterday as "a scandalous abuse of public funds." In a letter to several members of Congress, group president Anthony T. Podesta said the task force has no experience in the field and that the grant seems to be "a vehicle for the Eagle Forum to garner federal support to advance its controversial views."

Schlafly said the grant would help balance the $580,000 awarded last summer to the National Coalition Against Domestic Violence, which represents most of the nation's 877 shelters for battered women. "I thought fair play required equal treatment of traditional women," she said.

While there is a place for women's shelters, Schlafly said, "The feminist ideology is that all men would be wife-beaters if they got the chance. We do not accept that ideology. Surely the whole answer cannot be to punish the woman by taking her out of her own home."

An aide to Herrington said that Schlafly had "obviously been involved in some of the negotiations," but that "the grant stands on its own. The decision to award the grant had nothing to do with Phyllis. She had a hand in pushing the initiative along."

The aide also dismissed suggestions that the award was designed to offset the shelter coalition grant, saying "each of those are strategies that have to be pursued."

Earlier this year, Herrington's office drew criticism for awarding $186,710 to conservative activist James McClellan and a dean at the Rev. Jerry Falwell's Liberty University to write a high school course on the Constitution.

The new flap is the mirror image of last summer's controversy, when Attorney General Edwin Meese III held up the grant to the National Coalition Against Domestic Violence for several months after complaints from conservatives. Rep. Mark D. Siljander (R-Mich.), for example, said Meese should not be funding "proabortion, prolesbian, anti-Reagan radical feminists."

While the coalition's grant is to assist women's shelters, Schlafly's associates seek to educate the public about preventing family violence, to compile a directory of family services and to enlist civic groups in five cities to work on the problem.

The task force president is Tottie Ellis, a Nashville "right-to-life" activist who is national vice president of Schlafly's Eagle Forum. The vice president, secretary and treasurer are all Eagle Forum activists.

Ellis said the group would approach the problem "from a different angle" than feminist activists. She said Schlafly would play no official role but that "I will call on her for advice because I consider her a brilliant woman."

The group officially withdrew its application in April, saying that "grants of this kind should not be given" at a time of high federal deficits. The Herrington aide attributed this action to "a misunderstanding" caused by delays.