A group of 28 Fairfax County high school students, anticipating a long-planned study tour to Greece next month, has had to make a major change in its itinerary because of fears about security problems at the Athens airport, raised Tuesday by President Reagan.

Across the country, many other Americans who have been looking forward to a vacation in Greece also are facing the decision of whether to proceed with their plans. Many are canceling trips to Greece, say tour operators. Others have switched their reservations to another European destination. Most still seem determined to visit Greece, though some are postponing departure dates.

American Express, one of the nation's largest tour operators, said yesterday it is getting a "significant" number of cancellations for its holidays in Greece, although no specific figures were available. Globus Gateway/Cosmos Tourama of Forest Hills, N.Y., another large tour operator, estimated that 10 percent of its Athens-bound customers are canceling or taking a different tour.

Sun Line Cruises, which operates two luxury liners out of the Athens port of Piraeus, said it has had about 300 cancellations this week for upcoming cruises, a figure Vice President Alex Keusseoglou called "alarming." But the rush to cancel immediately following the president's remarks began to slacken by yesterday. The line's Stella Solaris and Stella Oceanis sail with about 1,000 passengers a week.

The line has waived penalties for canceling any of its cruises through Aug. 2. This permits passengers scheduled to sail later this summer to postpone making a decision without losing any of their reservation payment. Sun's hope is that the Athens airport problem will be resolved quickly and these passengers will decide to join their cruise.

Homeric Tours of New York, the largest charter flight operator from the United States to Athens, normally flies three times a week in the summer with its wide-bodied 747s "100 percent filled," and there's usually a waiting list of 50 left behind. But last night's flight, said manager Nikos Tsakanikas, was expected to depart with several empty seats because of last-minute cancellations.

Those who stay home face Homeric's cancellation penalty, which is 80 percent of the $550 cost of the flight, if their seats could not be sold. Such stiff penalties are characteristic of charter flights.

Until this week, the Fairfax students, whose ages range from 14 to 18, had planned to depart July 3 for a three-week, $2,100 trip to Italy and Greece, including a cruise to several Greek islands. Since Monday they have been attending special morning classes to study the literature, culture and history of both countries.

But after Reagan's warning about airport security problems in Athens following the hijacking of Trans World Airlines Flight 847, school officials began discussing alternative arrangements. Concerned parents also began calling in, asking, "What are you going to do?" said Maria Wilmeth, who heads the study program.

Yesterday, school authorities decided to eliminate Greece from the tour. Instead, the students and their three teachers will explore the ancient Greek ruins on the Italian island of Sicily. "It's disappointing," said Wilmeth. This was the first time Greece had been added to the study program, now in its fifth year.