They will never accept the existence of bitcoin.
Not agreeing with its existence is a better term to speak of. It's impossible for any governmental authority to not accept/acknowledge its existence, because they are well aware of how much potential there is. Back in the days they didn't take Bitcoin serious as they thought it would fade away after a while, but now they see that even the average person is starting to get involved in Bitcoin, and thus Bitcoin is starting to prove governments wrong, they realize that it's impossible anymore to think lightly about Bitcoin. Bitcoin offers people an escape from this rubbish system, and that's what people slowly but surely start to realize -- this is just the beginning of what has to come.