I'm Australian but FWIW some friends and I were talking about this over breakfast. I personally think that while it's a bit jarring from the outside, Americans celebrating the rebuilding of American spaceflight capabilities makes a lot of sense.
Also, it would probably be worse to have official communication policy restricting what people could chant on livestreams.
I think this is a large part of it. The Apollo program, and to a lesser extent the Space Shuttles, are not just historical events, but events that had a major cultural impact on the country. You cannot divorce the nationalistic response of people involved in this endeavor from the connection America's space program has to historical achievements we celebrate throughout our history classes in school. The successes of the spaceflight industry were always, from the beginning, tied to a sense of nationalism given the context in which it arose and delivered success. It's a unique industry in American culture, and I'm not surprised it's hard for individuals from other countries to immediately understand.
Also, it would probably be worse to have official communication policy restricting what people could chant on livestreams.