integrated circuits were only invented a couple years before the Apollo moon missions started in 1961
imagine an alternate timeline where that didn't happen, could moon landing have even happened with vacuum-tubes? highly unlikely
In between IC's and vacuum tubes, isn't there discrete transistor logic?
I think it would have been more likely to be some kind of mechanical analog computer full of gears and cams (which some planes and missiles did use for guidance). Probably needing more support from the ground.
Apollo did carry tubes also, in the radio transmitters.