Government is able to know the transactions you make when you’re making use of an exchange that is centralized. Centralized exchanges always make reports to the government, but decentralized exchanges has nothing to do with the government and they can never tell what’s happening on decentralized exchanges because they have no access to it and does not control it.
That's a fact. Centralized exchanges are submitting to government's demand when it comes to data reading but you don't have to worry if you have nothing to hind or something suspicious linked with your addresses. This is also why I use decentralized to sell my coins or trade because of the privacy I need although I have nothing to hide from anyone I just feel it very comfortable that no one sees what am I doing with my money.
So, if you don’t want the activities you’re into in the crypto community to be known by the government, it would be best that you start making use of decentralized exchanges, if not, then you’re still exposed to them by using centralized ones.
Yeah, also be aware of some decentralized exchanges some of them is under also centralized system where government look for data, much safer with complete decentralized exchanges.