Well we don't know if you can adopt an opposite policy of an already aquired policy, the assumption is that we will. I don't think theirs much difference in the two options other than you obviously wouldnt invest some culture for X bonus in X tree if it locked out Y Bonuses in Y tree that you want more. Personally I hope and think it will probably be the case that this is not the case, you will be able to adopt an opposite policy, all that will happen is that you will lose any "per turn" bonuses currently active on the other Policy, If at a later point you decided you wanted to use the abilities from the other policy again, you can switch back and the tree will be as you left it, mean while none of the opposing trees bonuses will be active. The cost of changing trees/policies to the opposite will be loosing out on all the bonuses you've spent large amounts of culture on, if you only ever brought 1 bonus from the tree your switching out of then that won't be much of a big deal for you, e.g you took honour and +1 free great general bonus (not a per turn bonus, so you dont care to lose it.) early on for some conquest but later on after not developing it any further you switch to the opposite policy tree loosing your "massively important" +33% bonus against barbs and can now utilise your new Policy. Depending on the culture invested will depend the loss on changing, all that culture could have been spent on a different branch you aren't switiching for a bonus you wouldnt lose, this is cost enough to avoid any anarchy charges.
If the choice is not their, i.e your choice for Honour as apposed to its opposite is permanent, then this will just exclude the "pay a little now for a decent current bonus and switch later or save the culture for a bonus you can keep till the end of the game" choice, not a big deal, but I assume that will not be the case and that small choice will still be in the game.
If the choice is not their, i.e your choice for Honour as apposed to its opposite is permanent, then this will just exclude the "pay a little now for a decent current bonus and switch later or save the culture for a bonus you can keep till the end of the game" choice, not a big deal, but I assume that will not be the case and that small choice will still be in the game.