In some regards, yes, certainly it is. In other regards, not so much.
We have a cold war going on between India and Pakistan, two nuclear powers, still, that involves nations housing 1.5 billion people combined.
We have a more and more polarized West that's basically fighting a bit of a civil cold war right now, "populism" against "progressivism" or whatever you'd like to call it.
Putin is the oldnew Enemy of every Western politician and pundit (exceptions prove the rule).
And we have a China that looks at all that and mostly quietly builds up their influence in the world, that one could consider a bit of an economic cold war.
Oh, and China is literally doing moonshots, too [1]. And so is India[2].
Yes, as both incidents are part of the political climate of the time, and are a part of history. They are not the proudest moments, but it is doubtful if, without the spectre of Communism or the USSR, the US would have tried to land on the moon.
Edit: Can anyone explain to me why this is getting downvoted?
Is there really a consensus that the current political climate is comparable to the cold war?
The cold war which is intertwined with the space race that put a man on the moon?