The White House has ordered cost-cutting revisions in proposed new rules for protecting textile workers against lung-damaging cotton dust, sources said yesterday.

The move, over strong objections from the Labor Department, makes the administration's own campaign for a stronger occupational safety and health program a principal battle-ground in the fight against inflation.

The directive was contained in a memorandum sent Monday to Labor Secretary Ray Marshall by presidential economic adviser Charles L. Schultze, who said he was acting on President Carter's instructions.

The Labor Department refused to comment. But it was understood that Marshall will appeal personally to Carter today to reverse the order, which critics say would substantially weaken the proposed rules by delaying engineering controls and giving employers broad latitude in choice of protective devices.

The Labor Department's Occupational Safety and Health Administration had been prepared to issue a final cotton dust exposure standard last week. It was to have been the culmination of a decade-l ong fight by textile workers to reduce the incidence of byssinosis, or brown lung, a debilitating and sometimes fatal disease that health experts have attributed to exposure to cotton dust.

But Schultze and other anti-inflation planners asked that the standard be held up for an assessment of its potential impact on inflation, prompting an intense two-week battle within the administration over whether the standard should be modified.

Schultze's directive was the strongest evidence thus far of White House efforts to examine governmental regulatory activities for their effect on inflation and clamp down when opportunities for cost-cutting are found. The Environmental Protection Agency is also under increasing pressure to relax some air pollution control requirements.

Marshall, in a memo to Carter last week protesting the delay, estimated that the proposed cotton dust standard would cost the textile industry $625 million in new euqipment and $84 million a year in operation. He said this was about one-quarter the cost of the initial standard that was proposed during the Ford administration.

The Council on Wage and Price Stability, in an earlier assessment, praised OSHA for reducing the anticipated costs but suggested that another $125 million could be cut without substantial harm to the purpose of the proposed regulation.

Schultze's memo came to light as the government appeared in federal court here to explain why it had not issued the cotton dust standard by last week. OSHA had previously told the court it would do so in arguments over a case brought by the Amalgamated Clothing and Textile Workers and the North Carolina Public Interest Research Group to force issuance of cotton dust regulations.

U.S. District Court Judge Howard F. Corcoran, expressing impatience with the delay told government attorneys he would order OSHA to issue the standard if they could not give him an exact date for its issuance by this morning.

"I am going to tell you that it had better be a very close date . . . " said Corcoran.

When a government attorney attempted to explain about the White House intervention and asserted that "we are now closer to promulgation of a standard than we were at any time in four years," Corcoran snapped. "That is not enough.When are you going to get the regulations out?"

Appealing for "no more excuses," Corcoran said, "This case has been kicking around for about four years mostly because the Department of Justice (acting as the government's attorney) and the Department of Labor want to drag their feet?"

As of late yesterday, government officials said they did not have a precise date for issuance of the standard. Attorneys for the workers groups said they would be ready to ask Corcoran today to order its release and Corcoran said he would consider the request "on an expedited basis."