The key is that each group should have representation proportional to their proportion of the population.
I don't quite agree on that, because that's not what a district-based system is supposed to accomplish. The goal of a district-based system is that each district has their own representative to represent the specific interests and desires of that district. If a state is uniformly 51% Democrat and 49% Republican, the result of this,
even if you don't do any gerrymandering at all, will be that Democrats will win 100% of the seats despite winning 51% of the votes.
If someone wants proportional representation, then go with proportional representation where everyone votes for their preferred party and then that party gets that percentage of the seats. (not many countries have fully proportional representation though, more commonly they have a mix of districts and proportional representation) I think proportional representation would be good to have, although I would still want some of them to be elected by districts because I think some representatives should have a real tie to particular areas--this might require an increase in the size of the House of Representatives, but whatever, the US has one of the largest disparities in the world when it comes to size of population versus size of legislature; there's little reason it can't double its size.
This is not to say, of course, that the goal of gerrymandering is to make it
less representative of population proportion, but a district based system is not supposed to nor should it inherently provide "proportional" representation. This idea also has the problematic effect of reducing all races to Republican vs. Democrat despite the fact that the candidates themselves do play a real role in the issue (this is one issue with proportional representation: The fact it turns it into
only the political party mattering rather than the actual candidates, though again this is mitigated by a mixture of proportional and districts, which I think the United States would be smart to adopt)