Giving money to a nonprofit is not a statement of absolute agreement with them. It is a statement that you value the work they are doing, and their presence. Being a Christian nonprofit does not require them to preach and prosthelytize.
People do all the time. A lot of large national charities are Christian organizations like Salvation Army, Habitat for Humanity, Goodwill, World Vision, and more. I listed those because most younger people today don’t associate them with their deep christian roots. Yet most of them were founded out of the teachings and ethos of the Scriptures that call us to care of our neighbors.
While a non-Christian would most likely not donate to a church, there are a lot of Christian organizations doing good things in their neighborhood, city, state, and world. For people passionate about the issue of homelessness the Salvation Army can be a great organization to donate to. Goodwill it a good place to donate lightly used clothing and household goods so that they can be used again by people in need.