At the current state of the world's politics, I don't think we will achieve a harmonious living relationship with each other even in the next 50 or so years. Countries are still power-hungry albeit doing it discreetly, seeking power sources here and there and making sure their enemies won't get to their objectives before they do. Also, we certainly don't need a unified religion since it's just something you hold onto when you don't want to face your problems head on.

I don't know what would bitcoin's role will be in a one-world government: the new authorities can just create a simplified, one-currency that people can use without having to trade it into a local currency. Bitcoin wouldn't be able to cater all this world needs if ever we shifted into a one-world government (hint: we'll never reach utopia). If anything, the world will crumble in the next generations knowing how ego runs in the veins of world leaders right now.