I view civil society as inherently cooperative rather than competitive. Whether you view government as a weed or not, privatizing traditionally public services by handing them over or contracting them out to for-profit institutions is a mistake. Picture civil society as a nice lawn and picture government and corporations as weeds. You do not get rid of the weed of government by making room for the weed of for-profit enterprises. But actually, I find the analogy of weeds to be misleading. It isn’t that we want to utterly abolish government or corporations, it’s just that a cooperative economy would require less of each to function properly.
And:
Take a public library, for example. The rightwing Civil Societarian (or libertarian) would suggest privatization, turning it over to a for-profit corporation (which would profit vis-a-vis government contracts or member dues, advertising, etc.) This corporation might be based anywhere in the world. The Cooperative (or leftwing) Civil Societarian would suggest turning the public library into a local cooperative run as a non-profit by the local community. How would this be any different than a public library based on taxation? It might not be very different at all, actually, except that it would be a voluntary enterprise rather than one reliant upon taxation.
I'm not quite as confident as Erik that his reading of Kling's notion of civil societarianism is correct.* It seems possible to treat government as a "weed" without making the only other option one of private enterprise. Kling clearly praises the virtues of the "private sector," but he can speak cheerfully of those aspects of it that are not motivated by profit. As he writes, "Katrina-ravaged New Orleans was let down by its Democratic mayor, its Democratic governor, and its Republican President. It was not let down by private-sector volunteers."
What's more, earlier in the same post Erik suggests that "Corporations are not a part of civil society, but neither are institutions funded by tax dollars." On that grounds, the "rightwing Civil Societarian" who wishes to reduce libraries to profit-generating corporations isn't simply wrong--he's an impossibility.
That to say, I'm not certain that the notion of "rightwing" and "leftwing" civil societarians is all that helpful. It seems like the point of being a civil societarian is keeping each institution in its proper sphere--let business be business, let the government govern, and let a thousand voluntary associations bloom in-between. If there is a "leftwing" and "rightwing" tendency, it seems to be largely a matter of preference in terms of where they choose to direct their skepticism.
The explicitly Christian option, if I may be so bold, is to look askance at both the government and business (yet simultaneously affirming their intrinsic goodness), and then go about filling the massive space in the middle with its own institutions and structures so that neither business nor the state need to do much beyond fulfilling their basic objectives.
I say "it's own" because the Christian option in the end forces us to also look askance at civil societarianism itself. Kling's final suggestion is that civil society might stand in as an appropriate object for our longing for transcendence that fundamentally marks society off as human. That is the turn from civic society to civic religion, a turn that compromises (for the Christian) the unique role of Christianity not simply as private belief system, but as metaphysical grounds for a truly civic order.
*Based on the posts Erik mentioned, at least. I haven't read much of Kling's stuff (alas) and am putting this out there in a hurry, so he may have written elsewhere on this that Erik knows of and didn't link to.