If you don't declare any of your hodlings in Bitcoin or profits, then they won't find out. But keep in mind that if they somehow do find out, you'll be paying back everything at once.
Coinbase has been the first (at least that we know of) to be forced by the IRS to share customer data. I am sure this is just the beginning of a wave coming from tax agencies all around the world locating black money holders trying to escape the system through crypto. Exchanges can go to court and say whatever they want, but eventually they will lose as the government has plenty of laws to hide themselves behind, and to use them in their advantage. Especially in times where the governments are chasing down black money streams leading to people financing terrorism.
It basically means that no matter what exchange we're using to buy or sell coins at, it might turn out that this information eventually will be known by the governments.
How about certain services that allow you to buy and sell coins where you only need a mobile phone number?
Even when governments make these services hand over all information about those that bought and sold coins, they only have a telephone number to start with.
In that aspect people can just buy a $5 prepaid sim card where they use this number basically to buy and sell coins.
No government will know who's behind this number since you can easily get rid of this card. But then again, if they play it dirty, they can even attempt to trace the signal of your phone...