Characters have their own histories which, of course, should have a huge bearing on their behaviour, attitude and general outlook on life. They should be shaped by the history of the country, town, world etc they belong to, whether they take the official line or rebel against it.
I don't think it is possible to be indifferent to history given it is the story of where we come from and how can you be indifferent to that?
Characters should reflect something of this too. They will react to history, personal, cultural or both, even if that reaction is a bad one. (It probably won't be bad from their viewpoint and it should be interesting to show how they've reached the conclusions they have and what consequences arise from these).
I mention history as my latest Chandler's Ford Today post is about becoming a heritage guide and ties in with previous posts relating to the Battle of Agincourt. This is being commemorated over two years due to the 600th anniversary and Hampshire's links with the battle. So here we have a historical story being brought back to life to bring in the tourists and all the benefits that brings to an area. Does your fictional world do something like this? What industries does it have? How does it use its history - honourably or otherwise?