Christianity is actually government-neutral, which contributed to it's early success in Rome and surrounding governments (after they stopped persecuting Christians, of course).
Judaism evolved as an anti-government effort, which is why it was perpetually beaten-up by other governments.
Islam started similarly to Judaism, with a struggle. But the catch there is that Mohammad actually won. So while they all started similarly (similar lore, similar timeframe, monotheistic), all three had distinctly different postures toward the government.