FRANKFURT, West Germany (AP) _ Anxiety about the Chernobyl nuclear power disaster has played into the hands of left-wing political parties seeking to upset a backer of Chancellor Helmut Kohl in a key governor's race leading to general election next January.

Opinion polls indicate a sudden surge in opposition to nuclear power that has brightened prospects for the Social Democrats and Greens Party, both of which have long opposed nuclear power.

''Not even the NATO nuclear missile deployment decision (in 1983) so emotionalized the German people,'' Walter Tacke, director of the respected Emnid Institute which conducted one of the polls, said Tuesday.

Kohl's center-right coalition government, which has been criticized as indecisive and disorganized, has insisted that fallout drifting from the stricken nuclear reactor in the Soviet Ukraine never was a serious threaten to public health.

But at the same time, several West German states, including one governed by Kohl's Christian Democrats, were banning consumption of fresh vegetables and milk that had not been inspected for radiation, and warning people not to play in the grass or swim outdoors.

Citizens deluged state environment and weather offices with requests for radiation readings and advice on whether they could take their babies outside or go on vacations.

''People felt they weren't being taken care of. They couldn't believe federal assurances that the radiation was harmless when they were being warned not to drink milk,'' said Eduard Heussen, spokesman for the Social Democrats in Bonn, the West German capital.

''What has happened is an affirmation of our drive for a phase-out of nuclear power plants and their replacement with safer alternatives,'' Heussen said in an interview Tuesday.

Opinion polls have suggested serious trouble for Kohl's coalition in a key state election next month in Lower Saxony, which was expected to be close even before the Chernobyl disaster.

Lower Saxony Governor Ernst Albrecht, a Christian Democrat, faces a Social Democratic campaign led by lawyer Gerhard Schroeder that has taken off over public alarm about Chernobyl.

German media commentators say that a Social Democrat-Greens defeat of Albrecht in Lower Saxony could build pressure within the governing coalition to replace Kohl for the national election campaign.

The Emnid Institute said that in a poll taken shortly after the April 26 Chernobyl accident, 69 percent of the 1,000 respondents opposed further construction of nuclear plants, compared to 46 percent in a similar 1982 survey.

It also said 60 percent of Christian Democratic voters queried felt the accident would damage Kohl's party, and that 53 percent of all respondents expected the Social Democrats and Greens to win a majority in the 1987 federal elections compared to only 36 percent in February.

''What is so unusual (in the recent survey) is this reaction that does not differ according to party allegiance,'' he explained.

''You see, the Germans have a deep-seated angst toward war and any problem that is a matter of life or death, affecting their health or environment. Radiation is so horrible because we can only notice its effects,'' Tacke said.

The government last Friday promised swift emergency aid to farmers who say they could lose millions of dollars worth of produce ruined by fallout or otherwise shunned by fearful consumers.

Farmers have long been a bastion of Christian Democratic votes in West Germany, and Lower Saxony is a major agricultural state.

Kohl and other government leaders say some state precautionary moves, such as warnings against swimming, were made with good intentions, but were exaggerated.

Last week, Interior Minister Friedrich Zimmermann dismissed the clamor for a phaseout of the country's 20 nuclear power plants. ''In our country, a jumbo jet could crash-land on a nuclear plant and nothing would happen to the reactor,'' he said.