Parishioners may write checks for small amounts or participate in minor ways. But most people don't come to church for social action. You'll need to find people of adequate means who will support your cause. UU's pride themselves on being democratic, and we may all be equal in the sight of God. But raising money is very different.
Some people have more money than others, and some people have significantly more money than others.
Don't be afraid to ask people for larger amounts. Generous people derive great pleasure from charitable giving. People give to people they know and trust, and will give when asked. Donors will also take great pride in what their church has accomplished. Plus, on a purely practical note, some social action issues are costly, and rightly so.