The political argument I support is that the activities of any religious organization should be divided between taxable “member benefit” activities (religious services / rituals / ceremonies, any other member-specific services or products) and truly no strings attached public goods, like food pantries / kitchens, homeless shelters, etc. When it’s unclear, the bias IMO should be toward a thing being member-benefit. In my city for example the Episcopalian church has a separately incorporated non-profit that runs the area food kitchen (an excellent one BTW). They are already set up for a possible future world where not all church activities are tax-exempt.
Where things get unclear is that on paper you can, say, give the hungry a meal, but unofficially, you demand that they first sit through a religious pitch or service or some sort. That is “strings attached” and benefits members in that it tends to produce new ones over time or at least gains a degree of control over members of the public who do not conform to their religious ideal (e.g., always sober, gainfully employed, properly bathed, upwardly mobile) so that the religious can tell themselves that they are accomplishing “good” or opposing “evil”. Indeed, simply getting someone self-sufficient by itself wasn’t enough to be considered success by many of these orgs. What real success looks like is a profession of newfound faith in Jesus.
To your specific questions, @CyberLN, in my experience and observation, yes there are differences between religious organizations for sure. The one I came out of taught that “all the world needs is Jesus” and that providing material needs leads to the dreaded “social gospel”, the idea that non-spiritual things like money, food, clothing or shelter in any way elevate a person or solve their problems. It has to be magic all the way down or it’s not legitimate and approved. So when we would (grudgingly) help people in practical ways, it was always after first debasing them, telling them what horrible sinners they are, how they must embrace Jesus in a way acceptable to us in exchange for any longer term assistance – and even then, it was assumed that if you didn’t at some point not too far in the future pull yourself up by your own bootstraps, there’d be an end to the largesse.
I am skeptical of the blanket claim that all religious orgs, on balance, are a net positive. It is, in my view, a case of selection bias: just because liberal religious groups happen to be the vehicle for a lot of social good, does not mean that their religiosity is a necessary ingredient for that to happen. They could just as well be lodges, secular charities, or ad hoc groups of Concerned Citizens. I think that houses of worship get way too much credit just by virtue of proximity and pre-existing social structures.
I don’t see a size-based difference; that is just a matter of scale. I see a difference based on the amount of illiberal zero-sum thinking baked into the specific ideology.