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Washington DC is League of Planets, Keeling is Planetary Union
It's a bit confusing, I admit, but an important difference. The Washington DC is part of the League of Planets navy. The PUV James Keeling is from the Planetary Union, which includes Earth, Mars, the Jupiter Net Colony and others. The League of Planets formed in 2519, led by the planet Satirli 6, which seceeded from the Planetary Union in 2489.
The Planetary Union is in many ways an extension of our current Earth cultures. More tech, certainly, but many things have continue on -- freedom of religion included. The League of Planets, on the other hand, has invested heavily in science, technology and education. The League considers religion to be a primitive and archaic belief system, and it has been outlawed. If you believe in things like gods, predestination, fate, etc., that's considered to be indicative of a lower intelligence. Hence, if you want to advance in education, business or the military, you'd do best to keep superstitious beliefs to yourself.
The League of Planets is not at war with the Planetary Union, but there have been significant conflicts. See the timeline in the back of the hardcover edition of THE ROOKIE to learn more.