Actually, other countries, including Canada, did ban distilled liquor for a short time circa WWI, in response to a worldwide grain shortage. Keep in mind you still had quite a few farm work animals to feed in those years. It didn’t last long and would not have lasted as long in the United States if it was enacted by simple legislation, not a constitutional amendment. A real good point here is that without the wars, the US is far less influential as a military power and Germany enjoys a much greater level of respect.On the other hand, with the US as but one of several great powers, why would the world follow their lead? Prohibition never really spread beyond North America, and it's likely that most Europeans would have seen it as silly.
On the matter of space, it is possible that it might be pursued as a prestige project by various nations, similarly to OTL. It might be fused with a pure science motivation, as was common in ante-bellum Europe.
It would be nearly impossible to forecast the progress of a space program in this ATL. We must consider the incredibly short interval between Sputnik and Apollo. Without the military incentive, who has the bankrolls? Howard Hughes was an aviator, remember. The prospect of spotting hurricanes and typhoons from outer space over the open seas would have huge multinational support.