There are a few things to unpack here.

The first is that, no, they can't directly trace your public key if you send ethereum as most exchanges have multiple wallets at least. Binance seems to have at least 3 for example.

Second, if you send an obscure token to an exchange like hitbtc then they might be able to track you because there might not be many depositors there or the only recent depositor could be just you.

Third, try not to send the same amount in and out of exchanges if you can help it (or similar) sending 0.987 btc into an exchange and withdrawing 0.9865 is going to make it fairly easy for someone to think both are from the same person regardless of anything else.