I think there are two major pitfalls that can easily be fallen into if you go into either a more radical 2K view or into a more neo-calvinist/Kuyperian.
In the radical 2K, there is such a sharp
divide between the sacred and secular. It seems to make things easy to compartmentalize--there's where/how I do my church stuff (all that faith, belief, practice), and over there's where/how I do my civic stuff (all my business, civic duties, etc). The problem is that there isn't always a clear divide. Many seemingly innocuous economic or business practices, for instance, could have moral aspects to them. How do we reconcile the moral aspects? Well, we look to our worldview, our faith as a basis for how we address these things. In dividing so harshly the "kingdoms" you run the risk of either being inconsistent (your civic witness seems to show little coincidence with your professed faith practice), or you're more in a no-man's-land, or even wishy-washy state of non-involvement.
Alternatively, you can swing the other way into more neo-calvinist/Kuyperian extreme which is more a
blurring of the sacred and secular - It could be boiled down to "If everything's sacred, then nothing is." This is where you get the caricatures of Christian media moguls redeeming outright-sinful (or in the least highly questionable on the conscience of a Christian) movies, or some of the attempts to "Christianize" people, places, things--you name it. I think this also under-girds more subtly some of the more broader evangelical tropes of making a 'Christian' item--if you slap a verse, a cross, or a fish on it...that being the baby-step version to really 'reforming' the whole system. I think this is a popular thing to grapple onto for younger generations who are all about changing the world, and the way to harness that 'youthfulness' for the church at large is seeming to be relevant to society....but instead of calling it 'trying to be relevant' (especially in Reformed circles, because we're not like those other evangelicals) we mask it in hyper-Kuyperianism and call it "redeeming."
I like to think that a balanced view falls somewhere in the middle of the two, recognizing that God's redemptive work is powerful enough to encapsulate the whole world--even caring for the lilies and the sparrows (so should we not also care for those things?)! That should move us to work his redeeming love in our lives--through "secular" and civic duties, even. However, there are specific, sacred acts that Christ has called us to be a part of--he is a holy God, after all, and so we shouldn't forget that holiness requires a 'setting apart'.
So, I guess, my response is:
Yes, the kingdoms are separate, but no, they are not. Hopefully that's not confusing as it sounds.
