Actually I have two objections to faith based charities - both of which you allude to above.
1 - Almost all faith based charities regard some form of evangelism (spreading the word etc...) to fall under "good works" and thus be a valid use of charity funds. I don't share this view.
2 - At least some faith based charities that I know of require the recipients to be involved in the religion in order to receive help (attending a church service for example). I think this is morally wrong, because it is no longer a free choice when you are holding something that the person needs.
Clearly there are many people not bothered by the above who want to support religious charities, and that is their choice, but I prefer to give to secular, humanist charities.
Also, many atheists do give to charity regularly, and I, at least, find it mildly annoying to have people constantly assuming that charity is always motivated by religion.