Nearly 300 textile workers and their supporters demonstrated outside the Labor Department yesterday against Reagan administration plans to review -- and possibly ease -- federal cotton-dust standards.

The demonstration here by the Amalgamated Clothing and Textile Workers Union and the Brown Lung Association was one of 36 held around the nation yesterday against the administration's drive to subject cotton-dust rules and other worker-protection regulations to "cost-benefit analysis."

Labor Secretary Raymond J. Donovan's announced on March 27 that his agency's review of the cotton-dust standards would include exploration of "all the alternatives, including the use of respirators," to protect textile workers from dust inhalation.

The regulations under review require respirators -- usually strapped face masks -- for workers exposed to cotton dust, but they also mandate that by March 27, 1984, textile firms must install dust-removal equipment to keep cotton dust at safe levels.

Nineteen of the demonstrators managed to get inside the barricaded building and into Donovan's outer office. Donovan at the time was in Chicago addressing a meeting of the American Newspaper Publisher's Association. However, a number of law enforcement officials were in the building, and theg gave the demonstrators a choice of leaving or being arrested.