They are entities that have a civic purpose, not for profit.
Yes, they can in some cases support political causes, that is normal.
You seem to have a narrow view of what 'community' is aka something is either a 'charity' or 'government' - the world is more complicated than that.
" That set of properties can and should draw significant criticism. " - no, the properties of fine.
They can be scrutinized like any organizaition: charity, private company, ngo, government, etc.