Why Reagan's trip to Peking would also help him at home

President Reagan is treading cautiously as clouds hover over his planned trip to the People's Republic of China next April. Despite Chinese objections, he has signed a bill passed by Congress authorizing a larger US contribution to the International Monetary Fund. But he has firmly dissociated himself from the amendment to the bill recommending that the ''Republic of Taiwan'' remain seated in the Asian Development Bank even if Peking is admitted. China strongly objects to use of the term since it regards Taiwan as a province of China and not a separate country.

The President is eager to see the China trip come off both for foreign policy and domestic political reasons. Despite his affinity for Taiwan, Mr. Reagan has gradually come around to recognizing the importance of a good relationship with the People's Republic of China. His visit to Peking would help restore a dialogue at the highest level for the first time since 1980.

The trip would also yield political benefits. Mr. Reagan has not had a major foreign policy success and, with an election looming, a journey to China with all the semispectacular media trappings it would entail takes on added importance. It would keep the President visible as a world statesman, dealing one on one with the major leaders on the global scene.

Contrariwise, if the planned trips - including the visit of Chinese Prime Minister Zhao Ziyang to the United States in January - are canceled, this would be seen as a setback to American foreign policy as well as to Reagan's image as a flexible pragmatist. The Democrats, political analysts say, would jump at the chance to criticize the Reagan administration for letting Sino-American relations deterioriate.

Such a development would be especially embarrassing to Reaganites, given the fact that the President has made such a turnaround in his public attitude toward China. Mr. Reagan campaigned on the basis of reestablishing official US relations with Taiwan, so he has moved a considerable distance from that position even though, as one US official puts it, his ''heart is in Taiwan.''

Neither Washington nor Peking wants to put the visits in jeopardy. But the Chinese have been unhappy with the IMF bill as well as another congressional resolution on the future of Taiwan which will come before the Senate in January.

Peking is also piqued by references which Reagan has made recently to the Republic of Taiwan, references seem designed for the President's right-wing constituency at home.

Administration officials believe that Chinese leader Deng Xiaoping is no less interested in having the Zhao and Reagan visits take place as scheduled. It is speculated that much of the recent public Chinese criticism of the President may be linked to internal Chinese politics. Deng has launched a campaign in China against ideological ''pollution'' from the West in apparent response to a Maoist counterattack on his modernization policies.

Whenever Deng's political adversaries want to give him a hard time, say analysts, they raise the subject of Taiwan. So Deng may not have the flexibility now that he normally does. ''He cannot afford to be cavalier on the subject of Taiwan,'' comments one administration official.

Other longtime analysts speculate that Taiwan is so delicate a political issue and that Deng himself feels so strongly about it that any apparent backtracking from the official US position has to be met with a response.

US Secretary of State George P. Shultz said Thursday that it is sometimes difficult for a country like China, with a different system of government, to understand that the various branches of the US government do not march in lockstep. It is for the Chinese to decide about the trips, he told reporters, but the President expects to receive the Chinese premier here and to travel to Peking. The US position remains that there is one China, he added.

Administration officials express regret that the Congress has taken actions objectionable to Peking at a time when relations have been on an upgrade and Peking has been leaning over backwards to be conciliatory. While it is not thought that the visits will be scrubbed, the problem is seen as a troublesome one.

In January the Senate will take up a resolution, sponsored by Sen. Claiborne Pell (D) of Rhode Island, referring to Taiwan as the Republic of China and affirming its right to determine its own future free of coercion by the mainland Chinese. Peking has protested the resolution as interference in its internal affairs.

Still another element of uncertainty is that some lawmakers in Congress want to adopt countervailing duties on Chinese textile imports, which could lead to Chinese economic retaliation. If the trips are canceled because of this and other issues, say China experts, this would put Sino-American relations into a cool period.

The White House is trying hard to avoid such a development.