Question:Since you do not believe that the church, out of the church treasury, can help non-saints, do you believe the church can help a saint that does not believe in some of these matters as you do?
The church is restricted to helping members of the church because that is the only example we find in the New Testament. Every case where aid was sent by churches, it was sent to Christians or to congregations to be distributed to Christians. See "The Work of the Church" for a list of passages.
Giving is a way to show that the giver and the receiver are in fellowship with each other. "For I bear witness that according to their ability, yes, and beyond their ability, they were freely willing, imploring us with much urgency that we would receive the gift and the fellowship of the ministering to the saints" (I Corinthians 8:2-3). When the Philippians supported Paul, he acknowledged their fellowship in his work. "I thank my God upon every remembrance of you, always in every prayer of mine making request for you all with joy, for your fellowship in the gospel from the first day until now" (Philippians 1:3-5). "Nevertheless you have done well that you shared in my distress. Now you Philippians know also that in the beginning of the gospel, when I departed from Macedonia, no church shared with me concerning giving and receiving but you only" (Philippians 4:14-15). This is one reason there is not to be a tie between the church and non-believers. "Do not be unequally yoked together with unbelievers. For what fellowship has righteousness with lawlessness? And what communion has light with darkness? And what accord has Christ with Belial? Or what part has a believer with an unbeliever?" (II Corinthians 6:14-15).
Though many claim to be Christians, not all teach the gospel of Christ accurately. "Whoever transgresses and does not abide in the doctrine of Christ does not have God. He who abides in the doctrine of Christ has both the Father and the Son. If anyone comes to you and does not bring this doctrine, do not receive him into your house nor greet him; for he who greets him shares in his evil deeds" (II John 9-11). It is not proper for a Christian or a church to support someone who is teaching false doctrine. Such financial support would show support for the false teaching. "And have no fellowship with the unfruitful works of darkness, but rather expose them" (Ephesians 5:11).
You are vague as to the differences in beliefs, but I am going to assume that you mean someone who teaches things contrary to what we find in the New Testament. "I marvel that you are turning away so soon from Him who called you in the grace of Christ, to a different gospel, which is not another; but there are some who trouble you and want to pervert the gospel of Christ. But even if we, or an angel from heaven, preach any other gospel to you than what we have preached to you, let him be accursed. As we have said before, so now I say again, if anyone preaches any other gospel to you than what you have received, let him be accursed" (Galatians 1:6-9). A person who will not abide in the teachings of Christ are not to be supported by followers of Christ.