I don't think the difference between buffer tubes is in the threading. i.e. any in spec AR receiver (and by inference, the XCR adapter) should be able to accept either a milspec or commercial tube. The difference is in the diameter of the rear portion of the tube, I believe. I think the milspec tube is slightly smaller. So, you want to match a milspec stock to a milspec tube/commerical stock w/ commercial tube, if possible. I think worst case scenario, you can put a commercial stock on a milspec tube (with some additional rattle), but I don't think you want to try to squeze a milspec stock onto a commercial tube.
So like I said, my understanding is that the RA adapter should be able to be used with either setup. Maybe Terra can come along and confirm.