Universalism is a great way of describing a challenge that is innate to all "nations". Actually, it raises a question: "is creating a new nation the best way of solving a Universal problem"?
In your example, it could apply as: is creating a new nation the best way to solve inter-national issues that Earth-bound nations couldn't solve in millenniums?
Knowing that's a too big question to solve within this context, we may need to solve a second most important question: how are we doing to affect that we are able to? One of the things that USA/Canada (and some other immigration based countries like Australia/New Zealand, etc) had some early "success" (mainly in terms of relative strength improvement as nation, not their treatment of indigenous people) was their ability to attract hardworking immigrants that was taking advantage of an "opportunity driven play field that allowed individual success". The fact that people gave up their old live and jump through hoop to immigrate to "new continents" actually says the expected "ROI" justifies the "oppportunity cost" of staying put. And such "high risk, high return" was mainly a function of those countries fundamental which was mainly shaped by their constitution, in conjunction with the resources available (again not to discount the indigenous people's sacrifice in such resources-availability).
So a constitution that recognize some-level of Univeralism is important (i.e. All people coming to this new nation, irrelevant of their other features, would be recognized as having basic rights been respected), on the other hand, some "exceptionalism" is also expected (i.e. The differentiating factors that set one apart from those who are not a citizen of the nation) is the main source of national pride and a key driving factor to "contributing to the nation - which is a collective pride of its members).
A constitution that is too "Universalism", would void its members of "differentiating factor", and devoid national pride; on the other hand, a constitution that is too "exceptionalism", would aliagnate people and likely deprive many people of their unalienable rights.
So, a balance and combined approach is necessary - unalignable rights (universal) should be recognized as core, and right portion of the constitution {a visitor can't be deprived of their right to live simply because they are not citizens); on the other hand, there would be "privileges" (i.e. Voting, being elected, service in certain posts, etc) that are reserved for citizens) - however, I would expect these to be flexible, as society evolves, some of the privileges may become moot, irrelevant, or newly developed).
In short:
Basic unalignable rights shall be universal,
Privileges shall be exceptional - a right for citizens that allow them to make a bigger impact to the save exploration of the space (or prevent threat from space) (i.e. If there would need a self-sacrifice pilot to man a mission to divert an incoming asteroid that is spearheaded by Asgardia, that pilot should be a citizen - the right to sacrifice oneself should be a privilege - however, that does not exclude inter-national cooperation that working with Russia/UK/US/China/India and allowing their astronauts to fly their portion of the mission.)
