The Atheist Madalyn Murray O'Hair sued NASA when the crew of Apollo 8 performed a reading from Genesis as they orbited the moon on December 24, 1968. She brought the case on separation of church and state grounds. Her case was eventually dismissed by the Supreme Court - O’Hair v. Paine, 397 U.S. 531 (1970).
Here's the District Court Judgement, the Appeals Court Judgement, and the Supreme Court Judgement.
It's not quite religious, but I think the idea of "Space Madness" is relevant. Prior to actual spaceflight, it was thought by many that being in space would cause people to just go crazy. Now, a lot of the given reasons for this were that the stresses and strains of space travel would cause people to snap, and also the idea that only crazy thrill seekers would volunteer to try in the first place. But there was also a sort of concern about the spiritual aspect too.
I'm getting this from an On the media interview with Matthew Hersch, who wrote on the topic. Here's a relevant bit from what he said in the interview:
Very common in that period was the idea that the mere act of traveling into the heavens, literally, would provoke crises of faith among the people who attempted it and that the result of this blasphemy would be tremendous guilt or some kind of religious mania that might manifest itself in homicide, even, as depicted in the film.
Among the proponents of space flight, it was actually hoped that the space age would actually be a religious experience that would reconfigure humanity's relationship with the divine, although leading space pioneer Wernher Von Braun did receive letters from children who were afraid that the rockets that he was sending into space in the 1950s would actually strike angels on the way up.
And he made it abundantly clear that he saw no chance that this would actually happen.
link to episode
http://www.onthemedia.org/story/176258-space-madness-real-and-imagined/
This lesson plan contains primary source documents (letter from a student and the White House response) that fits your question. It is the opinion of one person but does show the mindset of some people at the time. Her argument is that if God had wanted us in space He would have put us there. Since he didn't we could better use our time/money making the world better. I used this with my students to explore the rationale for the space race and have them determine if they thought it was worth it. Lesson Plan