So you get any of these bonuses and units regardless of religion?!?
No, but the religion they go with varies.
For example, in the real world, England is not an Autocratic government, but as the English player in a particular Civ game you can choose for it to be so.
Just like Christianity (in the real world) is the only religion with belief X, but in a particular civ game, Hinduism might be the only one with belief X or Islam might or (because you can rename religions) Buccaneerism might be the only one to give you belief X.
So as Buccaneerism spreads in a particular civ game, it will have a particular belief set that follows it.
The other issues are how the beliefs ARE tied to religion.
like the pantheon beliefs... they seem to be tied to your civ.
BUT if you develop a world religion, does that religion carry the Pantheon beliefs of your civ?
(and so any where your religion spreads your Pantheon belief overrides the native Pantheon belief)
When you develop a world religion, you get to assign the Founder and the first Follower beliefs (which I assume stick with the religion)
however
Can another civ (that follows your founding religion) be the one to add the second follower belief and/or the enhancement?
I assume the second follower belief sticks with the religion as well (when someone chooses it, it immediately benefits everyone that follows that religion.)
What about the enhancement, does it also "stick with" the religion? or can the same religion be different in different civs? (one has Christianity enhanced one way, another has it enhanced another way)....
Perhaps it might depend on "tech" or something like that, ie Christianity has a all 5 Beliefs, but some people only get the benefit of the first 3.