Just about every science fiction story I've read, once being colonize other planets they take their nationalism with them.
We are currently seeing a resurgent "space race" - though it doesn't get the attention of the USSR vs USA "race" during the Cold War. While the US is planning on sending an expedition to Mars sometime - the Chinese are planning on building a lunar {something}. Mining operation? Military base? Colony? All have been mentioned at various times by various Chinese sources.
Even now, though, satellites take nationalism into space.
So there is no reason to think it will be different when we get beyond Earth's orbit.