The national offices of the Presbyterian Church are funded, in part by a per capita assessment on every member. Per capita is assessed by each congregation, which is responsible for passing a fixed amount up the line to fund the presbytery, synod, and General Assembly work. A few congregations around the country withhold their per capita, or that portion which is supposed to go to the synod and General Assembly as a protest. In addition, a number of congregations don't pay their full per capita because they can't afford to.
The official position of the church is that per capita is not a tax – the church is a voluntary organization, no one has to pay. On the other hand, no one has a right to withhold per capita as a protest.
Presbyteries are responsible for sending the full per capita up the line. This rule was invented to cover impoverished churches more than protesters. If a poor church could not pay one year, a richer church would be expected to pay more and all the congregations would look out for one another. Sometimes, though, the presbyteries cannot or will not cover the missing per capita. This year, the shortfall is expected to top $400,000.
When a congregation withholds part of its per capita as a protest, however, the protest is lost if the presbytery simply covers the shortfall.
I think this is a loss for the whole church. The highest levels of the church should be constantly aware of grass-roots protest. If disaffected locals find their voice stifled this way, they are more likely to exit the denomination altogether.
Let the protests be show. Publish all the congregational names. We all need to know what's going on at the grassroots, painful and embarrassing though it may be.