When you ask God to bless someone, do they have to be a Christian? I doubt it, but I still want to ask. When someone says may God bless you, does He actually do it? Also, what do you think of Mother Teresa since she was a Catholic? Do you agree with her mission? Since you say that it's not the church's main focus to take care of the poor and that was her main focus.
"Now behold, Boaz came from Bethlehem, and said to the reapers, "The LORD be with you!" And they answered him, "The LORD bless you!"" (Ruth 2:4).
To bless is to give someone happiness. To wish someone well is certainly not a bad thing to do. One of the pieces of evidence of God's existence is the blessings He gives to all. "Nevertheless He did not leave Himself without witness, in that He did good, gave us rain from heaven and fruitful seasons, filling our hearts with food and gladness" (Acts 14:17). Thus, whether someone wishes another person blessings or not, blessings still do come. "Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom there is no variation or shadow of turning" (James 1:16).
God doesn't answer wishes or prayers just because someone asks. "Now this is the confidence that we have in Him, that if we ask anything according to His will, He hears us" (I John 5:14). What is asked has to be according to God's will.
Imagine being a clerk at a store that is robbed. Do you tell the robber "God bless you"? The answer should be "No." You don't ask God to bless someone who is clearly going against what God stands for. In fact, to do so would indicate that you approve of what the robber was doing. "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 10-11). This doesn't mean blessings are limited to just Christians, but still, we don't use blessings to encourage evil.
Mother Teresa led a self-sacrificing life and did much good among the poor in India. Yet good deeds are not what places a person in heaven. "Not everyone who says to Me, 'Lord, Lord,' shall enter the kingdom of heaven, but he who does the will of My Father in heaven. Many will say to Me in that day, 'Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?' And then I will declare to them, 'I never knew you; depart from Me, you who practice lawlessness!'" (Matthew 7:21-23). A person can do good deeds from a human point of view and still be lost because that person did not obey God. It remains a fact that the Roman Catholic Church's teachings do not line up with the teachings of God in the Bible in every case.
Jesus said, "For you have the poor with you always, and whenever you wish you may do them good; but Me you do not have always" (Mark 14:7). Poverty will never be wiped out in this world. Christians are to do what they can for those around them who are less fortunate. "Let him who stole steal no longer, but rather let him labor, working with his hands what is good, that he may have something to give him who has need" (Ephesians 4:28). This is the duty of each Christian, but God did not give the church the duty of attacking world poverty. Its primary duty is to spread the teachings of Christ. "To the intent that now the manifold wisdom of God might be made known by the church to the principalities and powers in the heavenly places, according to the eternal purpose which He accomplished in Christ Jesus our Lord" (Ephesians 3:10-11). In doing so, people are taught to aid the less fortunate -- so only indirectly does the church have an impact on poverty.