It seems to me that if the space race were occurring right now (an impossible hypothetical, I know), there would be loads of fundamentalists talking about how it's not natural and that god intended us to stay on the earth, ad nauseum.
Did the Space Race generate any backlash from the fundamentalist religious community?
hi! there's lots of room for more input, but FYI, there was a similar question the other day that you may be interested in
Were there any objections to the space program on religious grounds?
and this older one that's slightly related
To put it simply, no. A majority of Americans who were asked whether the government should "do more" or "do less" in space responded "do less" through most of the 1960s, and there was no clear divide along religious lines. The most vocal opponents of the Apollo Program were leftist groups (the SPLC, among others) who felt that it was an expensive boondoggle, and the money would be better spent at home.