The non-Communist governments of Southeast Asia are anticipating improved relations between the United States and Vietnam with a mixture of hope and concern.

Offical reactions have been muted to recent assertions by Ambassador to the United Nations Andrew Young that the Carter administration will "move forthrightly" to permit Vietnam to enter the United Nations and to begin negotiations leading to diplomatic relations.

Even though the State Department backed away somewhat from Young's position, Southeast Asian diplomats and officials generally accept that Washington and Hanoi will soon begin settling at least the most irritating of their differences.

These are, from the U.S. viewpoint, the issue of military personnel still listed as missing in action in Vietnam, and from Vietnam's stance, that the United States "heal the wounds of war" with $3.25 billion in financial assistance promised by the Nixon administration.

Optimists in the region believe that a Vietnam holding a legitimate U.N. seat and having open channels of diplomatic and economic exchange with the United States will be a more balanced Vietnam, less dependant on the Soviet Union.

The pessimists fear that once U.S. funds - either in the form of government aid or private investment - start pouring into Vietnam, a potentially wealthy country, their own development needs will be largely forgotten in Washington.

For economic reasons, as well as more pressing fears of Vietnamese aggression, the anti-Communist governments of Thailand and Singapore are pessimistic about the results of improved U.S.-Vietnamese relations.

The other three members of the five-member Association of Southeast Asian Nations - Malaysia, Indonesia and the Philippines - appear to be somewhat more hopeful, and are coming to their own terms with Hanoi.

Malaysia, which has been struggling against a Communist insurgency for decades, recently sent its first ambassador to Hanoi. The other Asian governments have reached diplomatic agreements with Hanoi but have not yet exchanged envoys.

Thai former Foreign Minister Thanat Khoman, now a foreign policy adviser to the military government that took over four months ago, expressed his fears over U.S. intentions in Vietnam. Responding to a comment Young made before he was sworn in, that it was "in our national interest to have them [Vietnam] a strong, independent nation," Thanat said.

"This statement was made without due consideration and demonstrated a lack of foresight on the part of Mr. Andrew Young. We, the Thai people, should watch this sort of statement carefully because it might be a harbinger of something that will happen in the future."

Commenting on Thanat's warning, a U.S. source here said he was "certain" that the Carter administration "will take Thailand's situation into very full consideration if it establishes relations with Vietnam."

Last week, the Thai military supreme command protested strongly to a Radio Hanoi charge that Thailand and Malaysia were collaborating in supressing their Communist movements and extending their espionage activities under U..S direction.

Thai military leaders continue to fear that the insurgency here, which has quickened since October's coup, eventually will win active support from Vietnam by way of neighboring, Communist-run, Laos.

Many diplomatic observers in Bangkok doubt that Thailand will take any positive initiatives as long as Prime Minister Thanin Kraivichien remains in office. Thanin, who leaves no doubts about his belief in a worldwide Communist conspiracy, has been meeting for the last three days with Singapore's visiting Premier Lee Kuan Yew. Through tough-minded policies, Lee has succeeded in virtually purging his tiny city-state of active Communists.

At an airport news conference before leaving today, Lee was asked to comment on the Carter administrations plans to improve relations with Vietnam. "I would hope their expectations of rational, cooperative, constructive relations will be fulfilled," he replied.

A joint press statement said Lee and Thanin had agreed on a number of bilateral economic programs and called for ASEAN as a whole to establish "an economic dialogue" with the United States, Japan and other developed countries.

With the anticipation that the United States will soon join Japan and Western Europe in competing with the Soviet Union for the favors of Vietnam, some regional economists believe that only by close cooperation can the non-Communist states continue to offer Western investors a viable alternative to the as-yet-untapped Indochinese nations.