Most people have an unfortunate tendency to project their own values and preferences onto the world at large, and fail to recognize when they cross the boundary out of their own spaces and into other people's.
Recognizing this means advancing solutions that primarily aim to minimize conflict among many parties, each pursuing their own particular concept of the good within their own boundaries, and avoiding trying to universalize any singular set of terminal values.
Attempting to pursue solutions that depend on everyone agreeing on the same set of terminal values will always fail, and will often generate intense conflict that escalates well beyond the bounds of the original question and causes a great deal of collateral damage.
Yes, that's called compromise. It's basically one of the foundations of society and civilization. It's not a blocker for public-interest projects.
Societies are not monolithic blobs with a singular "common good" -- they're complex networks of relations among different people with fundamentally varying worldviews and value systems. Making public-interests projects work entails respecting pluralism and individual autonomy. There's no alternative: projects that depend on conformity will inevitably fail.