Sorry in the circle example I forgot to say "with constant population density across the entire area."
Also - "convex districts" is one of the attempts I've seen to avoid small corridors and the like. Convex means "no pinches" after all.
Your example though is correct - any time you draw lines based on population density, you will get complaints about unfairness because of potential "ideological" density differences. Any time you draw lines based on "ideological density" you will get complaints about population density.
Consider this situation: how could you possibly construct a geographic district if you had a population that was 90% for one party, but 10% for a different party, but the geographic distribution of each party was homogeneous (that is, no matter what area you looked at, 9 people would be party A and 1 would be party B). If the districts were defined by geography, party B would "never" have any representation.
So the root cause is districts based on geography, period.
If we were serious about gerrymandering, we would remove all geographic boundaries from representation. In the US at least, you would also have to get rid of the concept of a partisan Executive branch. After all - we have problems as it is with our partisan executive, when our votes are generally split close to 50/50 for party A vs party B ( I consider 48% vs 52% to be essentially equally split), but representation is 100% or 0%.
Unless we change the executive to something that has no 'head' - where it is always proportionally representative, this problem will always exist.
And if you use proportional representation, you will always have some sort of quantization problem; if you had say 100 representatives, you would have no representation if you fell low enough below 1% of the total population. For a population as large as the US, that would mean over 3 million people that had no representation. Say you had 1000 representatives trying to decide all laws - you'd still have groups as large as 300k with "no representation" - you have to draw the line somewhere.
So for states - yeah gerrymandering can be a problem if you don't have enough total districts. If you have enough districts, gerrymandering doesn't work anyway. Or put another way: gerrymandering only works if you have too few districts and your population doesn't have enough geographic concentration of its ideologies.