Probably; the moon landings had the US' popularity skyrocket, firmly landing them in every history book worldwide. If they lose this second space race to China it won't undo that achievement, but it'll be embarrassing to the ego-driven people at the top right now (notably Trump and Musk himself).

Recently I saw someone claiming they voted for Trump because he hugged a flag once, and plenty of Americans proudly claim they voted for Trump so that he would "troll" their opposition.

Holy crap yes. Millions of Americans vote for a president based on exceedingly dumber reasons too.