The union representing several thousand employes at the Immigration and Naturalization Service plans to demonstrate its members' frustrations with a nationwide protest Friday about budget cuts and Reagan administration policies.

Michael Harpold, president of the National INS Council, said in a telephone interview yesterday from New Orleans that the protest will include informational picketing and distribution of leaflets and buttons saying "Bastante" (Spanish for "Enough").

"Ninety percent of our members voted for Ronald Reagan," he said. "We felt he would enforce our borders and address our problems at INS." Instead, he said, Reagan has proposed budget cuts for the agency and announced a new immigration policy the union considers "shallow and cosmetic."

Harpold said morale at INS is low because the agency has had no commissioner since the fall of 1979 and employes have been shifted throughout the country for months at a time to deal with immigration crises such as the roundup of Iranian students and the influx of Cubans and Hai-tians.

Harpold emphasized that the protest is not a strike. INS spokesman Verne Jervis said employes will be "perfectly free" to hand out leaflets and join picketing on their lunch hours or to take a day of vacation if enough employes remain to run local offices.

INS has about 10,000 employes. Harpold said his union, a part of the American Federation of Government Employes, represents about 5,800 INS workers, although only about 3,500 are members.

Jervis said his figures show the union has about 2,300 members of the 7,000 eligible to join.

The Border Patrol has a separate union, also part of AFGE, Jervis noted, but has announced no plans to take part in the protest.