True, the universal (small 'c' catholic) church of believers in Jesus Christ is not a religion. Just the opposite of all other religions in the world, in fact. But I don't think it's correct for one group to co-opt the designation and then condemn all other who don't call themselves by the same label. God sees the heart, man can only see the outside, therefor, labels mean nothing to the Lord.
On the face of it, it would seem a convincing argument. Yet, the one group did not co-opt it. It IS it. The splinter groups have splintered throughout Church history. The quitters (as it were - of the Church of Christ) do not get to identify themselves as if they are in full communion with the Church. There is one Faith. If you separate yourself from the Faith, then you separate yourself from the Church. Jesus Created His Church; it is individual men that have walked away from it.