There are food banks in every major city in the US which are not related to any church. Homeless shelters including ones that serve meals are in every major city in the country, Some are secular some are not. In Seattle there is
Fare Start, a restaurant that serves the homeless and trains them for jobs in restaurant business. It is not connected to a church and doesn't preach anything but how to get off the street.
Food on Foot is another secular program feeding the homeless. There are many of these organizations.
Now if you are specifically looking for atheist organizations starting up feeding programs, the
American Humanist Association began encouraging local Humanist groups to start feeding programs back in 2007. I don't belong to any organization, and atheists 'churches' are much newer than theist churches. So organized atheist feeding programs are only just beginning. You have to recognize most of us are not interested in atheist churches. Atheist volunteers are going to be spread out in secular volunteer programs.