Foreign tourists have taken advantage of relaxed travel restrictions in China to smuggle in thousands of Bibles and to contact local Christians, creating new official worries about one of the Peking's most ticklish social problems.

Recent travelers say Chinese officials have become aware of foreign tourists contacting or being approached by some of the estimated 500,000 practicing Christians still in China. Official media that had recently stressed religious tolerance are reemphasizing the importance of atheism and customs inspectors are again implementing restrictions against Bibles found in suitcases or in the mail.

A more tolerant official attitude toward Christianity, as well as Islam and Buddhism, had developed slowly over the past year. Peking has begun to display new sensitivity, however, to the small and often clandestine Christian groups that survive in some big cities and smaller communities along the Chinese coast.

Unlike Buddhism and Islam, which have been absorbed into local cultures in China over several centuries, Christianity is still seen as the product of a brief and painful invasion by European and American missionaries, traders and gunboats in the 19th century. Zhao Fusan, a fourth-generation Christian and associate director of the recently established World Religions Institute in Peking, said in March, "I think the time is gone forever to send missionaries to China."

Nonetheless, two European Catholic priests, one of them resigned from his order, and an elderly American nun have been admitted to China as teachers. All have avoided emphasizing their religious connection. Chinese authorities reportedly ordered the removal of a wallposter at Peking University that denounced the American nun as a "Vatican spy."

When Peking significantly eased restrictions on tourist travel in China in early 1978, part-time missionaries, including some Americans of fundamentalist Christian faith, began to enter the country.

One Canadian couple entered Canton on one of the first weekly four-day tours from here in February 1978 with a suitcase full of small Bibles printed in Chinese. They returned with the suitcase empty, a tourist who accompanied them said.

Other undercover missionaries followed, including some overseas Chinese who managed to distribute Bibles to their families and friends. Non-Chinese foreigners have found entering the country with Bibles easier, however, one clergyman here familiar with the process said.

"If you were in a tour group, and had a suitcase full of Bibles, the travel agent usually just shipped it to your hotel without any examination," he said. "They didn't expect non-Chinese to be making contacts inside China."

Chinese Christians have found ways to make contact with the travelers, usually through information supplied by relatives outside China. The clandestine distribution of Bibles has encouraged some Chinese to approach Western tourist at random and sound them out.

In Wuhan last month, an American woman touring a local university was startled when an English-speaking student, assigned to show her around, stopped at one point and asked: "Do you believe in God?"

The American replied: "Well, I think so."

The Chinese student, a 22-year-old woman, said: "I believe in God, too. Do you have a Bible? My grandparents are retired doctors and they believe in God. I would like a Bible, but don't send it because it will never get past the post office."

During a tourist trip through southwest China in April, a group of foreigners was approached in two different cities by Chinese seeking Bibles or conversations about God. Other tourists returning here have reported similar experiences.

The Rev. Jonathan Chao, director of the Chinese Church Research Center here, said that customs officials are now looking more carefully for Bibles carried by visitors from Hong Kong and enforcement of mail restrictions had resumed.

"People were sending Bibles to several friends or relatives inside China up to two weeks ago," he said, "but then a friend of mine sent about 200 Bibles over a week's time, and they all were returned to him undelivered."

Bishop K. H. Ting of the Nanking Theological College, one of several Christian leaders who are approved by Peking, said the government plans to publish its own new Chinese translation of the Bible in the simplified characters now used in China. The report by Ting, carried in a Lutheran paper, did not say how many copies would be produced or how they would be distributed.

European and North American clergymen, including some former missionaries, have been allowed to visit China recently and reestablish contact with some Chinese Christians they knew in Peking, Shanghai and other cities.

A recent conference of 800 religious leaders met under official auspices in Shanghai, and heard a pledge that religious organizations would be allowed to "develop normal activities." Most had been cruelly supressed after the radical politics of the Cultural Revolution began in 1966.

Visitors have reported government promises that some churches will be reopened in large cities. Since 1966 only two churches, both in Peking, have been allowed to hold public services. A report that Jesuit teachers would be invited back to reopen a medical college about 100 miles from Shanghai has been discredited, however.

In 1949, when almost all churches in China were shut down by the victorious Communist Party, missionaries estimated there were about 3 million Catholics and 800,000 Protestants in China. "No one knows how many there are now," said Chao, "but one could estimate 500,000 to one million."

The Rev. Peter Tchao, director of the Vatican Radio's Chinese-language service, recently announced an expansion of programming after visiting China. "I have discovered that we have a solid audience - not just the faithful but also youths who simply want more news from abroad," he said.

English students in Canton have also reported listening to a fundamentalist radio show, but emphasized that they rejected the religion and only wished to improve their American accents.

Ewing W. Carroll Jr., a Methodist minister living here, has been promoting a liberal Christian approach to China, supporting social progress without challenging Marxist commitment to atheism. His China liaison office of the Methodist Board of Global Ministries publishes a newsletter reporting sympathetically on Communist activities in China.

After a visit to China in March, he wrote: "China is not likely to open its doors to missionaries, but the door is already wide open for religious believers and Chinese Maxrists to meet on common ground."

He underlined a recent description of Notre Dame Cathedral in Paris by a People's Daily writer. The Communist writer said the church expressed "the passion of the builders for a life that is beautiful and good."