Sometime after the return of Apollo 11, Neil Armstrong visited the USSR. I wonder why he was alone? Weren't the other astronauts invited or they refused to visit? Was it because Armstrong was an atheist while the others were devoted Christians?
Religion as a motivation for Armstrong's solo visit is very unlikely. Armstrong was actually the 2nd U.S. Astronaut that travelled to the Soviet Union - the first was Frank Borman, who arrived in Moscow on July 2nd, 1969 after being invited by the U.S.S.R. Institute for Soviet-American Relations.1 Borman was among the more religious of the Apollo astronauts, and the Soviets certainly can't have missed his reading of Genesis when Apollo 8 was orbiting the Moon on December 24, 1968.
Like Borman, Armstrong was not invited by the Soviet government - his visit was arranged through the International Council of Scientific Unions' Committee on Space Research (COSPAR). Armstrong was part of a delegation of 32 American scientists and NASA officials2 and was ostensibly there to present a paper titled "Lunar Surface Exploration" at the 13th COSPAR conference in Leningrad May 20th through May 29th, 1970 (which he also subsequently presented at a conference in Berlin the next year).3 The official Soviet government response to his visit was a luke-warm, and it took 5 days after his arrival to get permission to visit the Kremlin.4
Most likely, Armstrong's visit was a natural result of the attempts of the heads of both the U.S. and Soviet scientific communities to develop a more cooperative relationship than had characterized the early space race. Several months prior to Armstrong's trip to Leningrad, Thomas O. Paine (Administer of NASA at the time) had sent his counterpart at the Soviet Academy of Sciences Mstislav Keldysh a copy of two reports on the possibility of creating a more cooperative relationship between the two agencies.
In keeping with the spirit of the Space Task Group's report, Paine transmitted copies of it, together with NASA's more detailed report America's Next Decades in Space, to the Soviet Academy of Sciences. In his cover letter of 10 October 1969, Paine told Keldysh that these documents might "suggest to you as they do to me, possibilities for moving beyond our present very limited cooperation to space undertakings in which the Soviet Union and the United States could undertake major complementary tasks to the benefit of both our countries."5
Their correspondence eventually led to a meeting in New York between Paine and Anatoli Blagonravov, chair of the Soviet Academy's Commission on Exploration and Use of Space, where Paine mentioned that Armstrong would be visiting the COSPAR meeting.
The amiable conversation touched on many subjects. Paine mentioned to his guest that Neil Armstrong planned to deliver a paper at the COSPAR meetings scheduled for 20-29 May 1970 in Leningrad, and Paine said he hoped that Armstrong would have an opportunity to visit some of the Soviet scientific facilities. Blagonravov responded that the cosmonauts would be pleased to show their American counterpart their facilities and some of the other space-related institutes.6
This ultimately formed the basis for the Apollo-Soyuz program, so it is entirely possible that Armstrong's visit was engineered specifically toward the end of fostering goodwill during the tenuous early phases of establishing a scientific relationship.
1 National Aeronautics and Space Administration. Astronautics and Aeronautics, 1969 - Chronology on Science, Technology, and Policy, p 195
2 National Aeronautics and Space Administration. Astronautics and Aeronautics, 1970 - Chronology on Science, Technology, and Policy, p 176
3 Armstrong, Neil. University of Cincinnati Résumé, September 1975, p 2
4 Hansen, James R. First Man: The Life of Neil A. Armstrong, p 582
5 Ezell, Edward and Linda. The Partnership: A History of the Apollo-Soyuz Test Project, p online