No, feeding the poor is not a primary mission of the Christian church.
When the Early Church fed the poor, it was the poor who were believers. Deacons were set up to feed the poor among believers.
Feeding the poor in society who are not Christians is something that the Christian church should not do (unless it is for evangelistic purposes).
Jesus Christ did not try to help the poor when He came to the earth. Jesus never ever fed the poor as a way to “help the poor”. WWJD?
St. Paul did not try to decrease poverty as a part of his Christian mission.
Reduction of poverty is not the mission of the Christian church.
Those so-called Christian leaders who centralize helping the poor are in the wrong and are not good servants of God.