Can the church and the press, two insititutions of American life that have not always seen eye to eye, find common ground in the need to protect themselves from current threats to the First Amendment?

That question engaged more than a dozen experts from both disciplines in a day-long conference here earlier this week. The conference was sponsored by nearly a score of press and Protestant, Catholic and Jewish groups.

Among other things, the First Amendment specifies that Congress shall pass no laws "respecting an establishment of religion or prohibiting the free exercise thereof, or abridging the freedom of speech or of the press." t

Allen H. Neuharth, president of Gannett Co., Inc., a newspaper broadcast group, and also president of the American Newspaper Publishers Association, acknowledged that "there are times when the press and organized religion view one another with mutual suspicion."

Nevertheless, he said, "the danger of big government power is the most serious threat to our free society today, as much of a threat to the free exercise of religion as it has become to the free press."

Jack C. Landau, Suprememe Court correspondent for the Newhouse newspapers and director of the Reporters Committee for Freedom of the Press, said that "there is no question that the fear of litigation fees is making newspapers more cautious . . . They are being much more cautious in stories that may involve being subpoenaed."

In general, he continued, the Supreme Court decisions of the last 18 months have set up the conditions that "are imposing quite a damper" on the press.

Dr. William P. Thompson, a laweyer and chief executive officer of the United Presbyterian Church, described the First Amendment problems for religious insititutions. For churches, he pointed out, the problems arise less from court decisions and more often from imprecise or improper legislation and from incursions by administrative agencies.

"Most often it [the errosion of religious freedom] assumes the form of government's presuming to divine what is or is not religion or religious activity," Thompson said.

He cited as an example the Tax Reform Act of 1969, which narrowed religious tax exemptions to "churches, conventions and associations of churches, their integrated auxiliaries and exclusively religious activities."

Thompson pointed out that these catagories "were not defined and were not limited in their application to relief from the obligation to file financial reports," which has caused continuing confusion in church circles.

Thompson faulted Congress for trying to deal legislatively with religious issues. "The House of Representatives has maintained a high interest in legislation which would regulate lobbying and related activities of churches as well as others," he said. "Many congressmen are apparently unimpressed by the contention of representatives of churches that such legislation would abridge First Amendment rights."

Thompson also cited a list of instances in which the power to tax or exempt from taxes was, in his view, improperly used to impair the free exercise of religion.

He acknowledged that the government "cannot permit any and every course of behavior claimed to be religious activity." Churches, he said should "freely accept those laws which have general application to all the people: laws relating to public health and safety and prohibiting criminal acts.

"But we have the duty in this land to use those means open to us, including communication with legislators and litigation in courts," to get government officials to search for the appropriate limits on the privileges of religious groups that are protected by the First Amendment, Thompson said.

In the day-long discussion, there was little agreement on whether the church and press should join in their First Amendment battles.

Osborn Elliot, dean of the Columbia University Graduate School of Journalism, summed up the ambivalence that many felt. When the conference was first proposed, he said, "I had felt that the press had become such a special pleader that people were turned of -- that it would serve the press very well to have the pulpit pleading its cause."

But on more reflection, he continued, "I have some second thoughts . . . I have the viceral feeling that the press should fight its own battles."

While there was no move to form any joint church-press committees to further their cause, others indicated that it was useful for both to gain some understanding of the other's problems.

"Whether members of the press or the church or both -- or neither -- "said Neuharth, "all Americans must unite and fight to preserve [First Amendment] freedoms. In the press, we can do that from the front pages of our newspapers to the last page, from sign-on to sign-off. In the clergy, you can do that from the invocation to the benediction."