I'm afraid I don't really have answers, only more questions, but hopefully thought-provoking ones.
The consensus seems to be that the space program continues. I agree, it would, but do you think it might start to see protesters a la the Vietnam War? And, if there starts to be an "anti-space movement", they'd probably still be in the minority, so what does the mainstream think of them? Do they believe them to be misguided, or "dirty commies", or what?
Also, on a more frivolous note: how long before the fringe/conspiracy theories start? Do people immediately start thinking that maybe the whole thing was a sham and the government secretly killed the men to hush them up? Or that they encountered something deadly on the moon and the government is denying it like they do with UFOs? Or does it take time before that kind of thing creeps into public consciousness?
I'm wondering, too, if this has an impact on pop culture. Star Trek's already been cancelled by this point, I think. I'm wondering if it would still go into syndication, or if people might not be as receptive to it, after the tragedy. Does David Bowie's Space Oddity get pulled off the shelves? How would that impact sci-fi and music, respectively?