Unity is between believers, not structures nor systems nor ecclesiasticisms. And there are the churches that probably could not have successfully gathered under the same roof, such as Jerusalem and Antioch, but still they were united in Christ, separated but not divided. We all know Christians with whom we had rather not work. They are there and we are here, and it is better that way. But we love and accept each other, separated but not divided.
Separatism dictates no fellowship, no association, no cooperation, no recognition.
While we may not be able to do everything together, we can surely do some things together. Differences, mostly those passed along to us by our forebears, may keep us separated, but they do not have to divide us in heart and mind. It is being against another that makes for division, while separation may only be circumstantial. Most blacks, for example, do not care to assemble with whites, and many poor Christians are not comfortable in rich churches. Separation without division is, therefore, possible so long as no one is against anybody.