The Reagan administration yesterday announced that the United States was dropping import quotas on shoes from Taiwan and South Korea despite bipartisan political opposition and industry estimates that the action could eliminate 36,000 U.S. jobs.

Among the states expected to be hardest hit by the president's decision are Massachusetts, home of House Speaker Thomas P. o'Neill Jr., and Pennsylvania.

Los Angeles County, in Reagan's home state, has 5,000 shoe industry workers, the largest concentration of shoemakers in any county, an industry official said. There was no immediate estimate of how many jobs might be lost there.

White House spokesman David Gergen said President Reagan's decision against extending the four-year-old quotas was in keeping with the administration's free trade policy. But Gergen said the decision was "a tough call" for Reagan because the president was besieged by congressmen, senators and governors from shoe-producing states urging him to keep the import restrictions.

Sen. Edward M. Kennedy (D-Mass.) yesterday called extension of the quotas vital to the health of the nation's shoe industry. A spokesman for O'Neill said, "I can't see how it could be favorable to American shoe producers."

The footwear decision was the second major test of Reagan's trade policy. Earlier this year, the president sided with those pushing for "voluntary" auto import quotas by the Japanese. Gergen defended the Japanese auto decision, saying it was in keeping with the president's free trade policy because the Japanese had requested the action.

"The Japanese moved on their own under threat of strong restrictions" from Congress, Gergen said.

The White House said Reagan decided to let the shoe quotas expire at midnight last night because the move would be anti-inflationary and the domestic shoe industry is strong enough to withstand the competition. The White House also said the decision would improve relations with Taiwan and South Korea.

"This morning President Reagan decided to reopen America's trading lanes as far as footwear" is concerned, Gergen said, but added, "I would not read it as a way he would come out on any case."

The American Footwear Industries Association disputed Reagan's claim that American shoemakers can withstand the competition. The impact of the decision will be difficult to quantify, said industry spokeswoman Fawn Evenson. But she said if current economic trends continue, the industry could lose 24,000 of 150,000 direct manufacturing jobs and 12,000 of 75,000 jobs in the shoe supply industry.

In 1968, when the American industry began to feel competitive pressure from the Pacific, the industry employed 240,000 workers in direct manufacturing and 120,000 in supply. At that time there were about 700 American shoe companies, Evenson said. Now there are about 300.

In Massachusetts, shoe industry employment has dropped from 30,300 to 12,300 since 1968, Evenson said. Shoe industry employment in Pennsylvania has dropped from 25,100 to 12,300 during the same period, she said.

Sen. George J. Mitchell (D-Maine) predicted Reagan's decision could eliminate 3,200 jobs in Maine.

The American Footwear Industries Association estimated the industry would lose $60 million for every one percent of the market lost to imports.

But Gregen insisted the employment impact would be minimal. In addition, he said, the lower-priced shoes, in which Taiwan and Korea specialize, should be even cheaper as a result of the president's decision. Gergen said Taiwan and Korea have been shipping their higher-priced shoes here to make up profits lost by volume. Taiwan has predicted the average price of its shoes should drop 12 percent to 15 percent.

The International Trade Commission, which makes recommendations to the president on certain trade issues, in April said the orderly marketing agreement with Taiwan should be extended for another two years, except on athletic footwear, and such agreements with Korea should be dropped.