Galations 6:10
Therefore, as we have opportunity, let us do good to all, especially to those who are of the household of faith.
The Bible says we are to do good to ALL , especially other believers.
I believe the church's primary obligation is to take care of needy people within the "household of faith" i.e. body of Christ, before we venture out to unsaved people.
And just because you do not know of any religious organization or church that is helping the needy by giving 1/3 tithes, it does not mean it is not happening.
Where I live, almost every big church has invested into opening centres for the needy, elderly, retarded and kidney patients, with full financial support from church members. These centres do not restrict services only to Christians but anyone outside of church that need help.
If your church holds an AGM, they will make transparent such plans and be accountable so that you know where tithes and offerings are going to.
I don't think a believer is more worthy of help than a non-believer.
Consider the parable of the good Samaritan - Samaritans and Jews had prejudice toward each other, but Jesus was trying to teach us to love, no matter what.
Good point about how some religious organizations may be doing a lot for those in need. I also can appreciate what you mentioned about ensuring the organizations we donate to display financial transparency.
I have been raised in the Mormon/LDS church, which leaders' HIDE finances.
They require 10% of all members who want to be considered temple worthy.
They changed the wording from "increase/interest" to... "income."
This way, they demand tithing even from those who are poor and not in the position to help others, let alone themselves. Yet, they tell members they will go to hell if they do not pay tithing, & that it should be paid first, before anything else & then they will be blessed. No suprise how many bankruptcies Mormons experience!
Another problem I've found with the church I've belonged to for so long, is that the leaders have purposefully tried to deceive members by not including Deut 14:28-29 (which states 1/3 of tithers are for the poor) in LDS scripture topical guides & LDS bible dictionaries. Not a penny of tithes go to the poor, which they have reminded members, & have regularly reminded members to not only pay tithes (10% of their income) but also to be generous in other donations.
If I or my child were one of the almost 1,000,000,000 starving, I would want someone standing up for us, to help us so we can help ourselves & eventually even help others. I think about how much just the LDS church could do if they showed integrity by following Jesus' example & Deut 14:28-29 by sharing at least 1/3 with those in need. I doubt they will do it, because they are entrenched in tradition & answer to nobody... LDS leaders are like worshipped gods.
So, I hope & pray LDS members will follow the commandments themselves, especially the 2 greatest commandments, which are to love God (& as we love others we love God) & to love others as ourselves... "on these 2 commandments hang all the law and the prophets." -Matt 22:40