As a general rule, isn't it true that, no matter what the INCOME demographics are, throughout the Western-culturally influenced world, large cities are fairly liberal / progressive, and small cities and towns tend to be more conservative?

This is an unworkable over-generalization. Asian countries can be much more conservative in many social ideas in all demographic areas whether large cities or small towns and rural areas. The whole state of Hawaii is very liberal whether it’s the metropolitan area of Oahu or the rural outer islands. Ireland tends to be liberal in all areas from Dublin to the countryside. Scandinavian countries are also liberal across the board. It’s best not to generalize.

I wonder how much gerrymandering of State and Federal districts have to do with the fact that, while the large cities in districts are progressive, so many of the representative seats end up with conservative candidates being elected?