Blatant liberal that I am, I've spent a lot of time listening to friends and associates go off about conservative Christians attempting to "hijack" the US government with their own values and outlooks.
The truth is people generally want to see their government reflect their own values. Sometimes they express this more subtly, supporting or opposing particular pieces of legislature according to their own beliefs. Sometimes they are more organized, and sometimes whole religious groups move toward specific governmental goals.
Christianity is certainly no stranger in this movement. The Baha'i Faith, for example, strongly supports the idea of a single world government working toward the betterment of all people rather than being dedicated to the welfare of people within certain geographic borders. The Raelians go even farther, envisioning a united world able to function without money in a system they call paradism, where robots will do most of the day-to-day work, breaking down the need for social classes.
The fact of the matter is religions commonly work toward their own vision of the greater good. When they work toward changes in government, it is less about proving themselves right and more about being driven by the belief that their ideas are what is ultimately best. Of course, non-believers will frequently disagree, which is one of the underlying reasons why a united world is a long way off, if it ever happens at all.