Mnuchin can try doing some thing against bitcoin, we all know how it would result. And for the fear of over-regulation, you don't have to worry for now, as regulating bitcoin is still hard as people are breaking their brains behind it.
Also I had read someone speak about this question a few years ago and I am going to quote him, because it is a wonderful post and makes absolute sense. Here :
Needless to say, it all depends on your transactional information. Swiss Banking is not 100% anonymous. It is still regulated and if push-comes-to-shove (read: legal), your details can be given out by the Bank.
Bitcoin is anonymous of course, provided your shield your wallet information well. If you want to pay me, and I happen to know you, when a transaction is done into my wallet, your wallet ID will be known to me. This is one way I can keep track of you. You could cascade wallets, keeping your original wallet information secure, but if I were to look at the transaction history of wallets, I would still be able to track back.
It would be anonymous only if I did not know who you were, and then we conducted the transaction.
There is no authority that would give your wallet information details out (per se). If you have an online wallet, the wallet provider may be required to give out your email address to which the wallet is associated with, other than that, nada.
Your best bet would be to have an off-line wallet, where you store all your money and for anonymous transactions, make a few online wallets and transfer money to these wallets for purposes of transacting.
For making an online or offline wallet, your personal details are not required.