Is secularism a real thing, or just a category of the mind, since nothing exists outside Christ's kingdom?

You have to answer it from two perspectives. From the perspective of heaven, yes, everything is Christ's reign, because there is nothing outside of Christ; he is the big sphere that encompasses it all, and inside you find larger spheres close to him and little spheres very different in size, shape, and color. That is ultimately how you want to look at it. But sometimes you cannot speak from the absolute sense; you have to speak from your own perspective inside the sphere you occupy, especially when you compare yourself to other little spheres. As for secularism, it depends on your definition. Secular usually means something with no religious attachment, people who live day to day without thinking about God, atheists, agnostics, and so on. The tendency of a society as its population grows is to drift toward secularism rather than religion, because the larger the population that is not educated to God, the greater the secularism, and that secularism ends up at odds with religion. The devil himself is the worst secularist, because he tries to look as much like Christ as he can while going by whatever the forces opposed to God want.