The local church not only has the responsibility to supply the spiritual needs of the members, but also the physical needs. If you remember, at the beginning of the church the members of the church in Jerusalem had all things in common and made sure that nobody was missing anything they needed. The church even daily supplied their widows with food (Acts 6).
Now this is one of the areas where it is easy to go too far in implementing. Many churches provide exercise equipment to supply the health needs of their members. Some provide sports programs and fun events for young people or singles, or other groups in an effort to supply their emotional / social needs. But as we read the scriptures, we find the mission of the church to supply the saints is more limited than that.
In 1 Timothy 5:16 it says,
If any believing woman has relatives who are widows, let her care for them. Let the church not be burdened, so that it may care for those who are really widows. (ESV) The church is only to supply for those who really need it. Nobody really needs the church to supply their exercise or social needs (outside of the relationship that is supplied by interacting with our brethren when we meet as a church). They should take care of these needs in other ways.
I have stated that the local church is to supply the needs of its members. I mean by that, specifically Christians in the local congregation. Some of the commands and examples of supplying physical needs are found in: Acts 2:44-45, Romans 15:25-27, 1 Corinthians 16:1-3, 2 Corinthians 8:1-4, 2 Corinthians 9:1; 12, and 1 Timothy 5:3-16. Some of these passages extend to Christians outside of the local congregation. When a local church has members that are in need and cannot supply those needs, it is proper for other churches to send money to those churches to supply what is needed.
Universal Church (individual Christians)
Nowhere in the scriptures is there any hint that a local church should supply the needs of anyone who is not a Christian but you could say that that is the duty of the universal church as individual Christians helping others. In the “Sermon on the Mount” that Jesus preached, recorded in Matthew 5-7, we find that individual Christians must give to those who beg from us (Matthew 5:42) and it does not restrict this to Christians. In James 1:27, we find that individual Christians are to take care of the widows and orphans (not restricted to Christians).
So then, as we have opportunity, let us do good to everyone, and especially to those who are of the household of faith. (Galatians 6:10) (ESV)