Sure and I'm glad that those organizations have worked well for you, but I've also seen these type of charities abuse the fact that they're the only help in town and use it as an excuse to proselytize to people.
And they're not the only charities in towns. A lot of the time there are other organizations that are secular that they also help. I prefer these because to me there is less of a chance of abuse
As far as church is being tax-exempt, I don't want to get into it, but it's extraordinarily abused. All you need to do is look at Scientology and Mormonism. On top of that, the Catholic Church also gets a huge amount of money from parishioners, and not all of it flows back into the community.
If they operate cleanly as a 501 3c non-profit, then I think that's fine.