That set-up is true, more or less, for most denominations. And it is often the case that the local congregation can sidestep some of the mistakes made at the higher levels, usually by simply ignoring them. However, I sympathize with those people whose consciences cannot do that for one or more of the following reasons--
1. The wrong, whatever it is, typically is shoved in their faces by the denomination's publications and communications, even if the local pastor never says anything about the issue.
2. The denomination gets known by society as having endorsed that wrong, even if the local unit/congregation and the individual member oppose it. Therefore, the individual member is identified by the average onlooker as having accepted whatever the particular wrong happens to be.
3. The local church supports the district, conference, diocese, national church, or all of them, with its financial contributions. Therefore, the individual member of the local congregation is put into a bind of either not contributing to the local unit in order not to finance the higher-ups who have gone wrong, or else swallowing hard and going along anyway, contributing the usual amount, even though he is thereby supporting with his money the wrong that offends his conscience.