I think that none of the banks will accept btc. They control the money, with btc can't do that, and this is something they try to avoid. And if this happens one day , this day will be not far soon.
Some banks are already accepting bitcoin and I'm sure there will be more of them in the future. I personally don't think there is a kind of conspiracy against bitcoin. People who run banks are businessmen in the first place, so when they see something is profitable for their business they accept it.
I don't know which banks and where Bitcoin is accepted. In my country banks are not accepting Bitcoin. I heard that Japan allowed Bitcoin is a legal currency and their people can do business with Bitcoin. So I think in Japan banks may be started to accept Bitcoin. I am not sure it's just my opinion. Becasue the govt is already accepted BTC means Banks also accept right.