Under their US license terms Coinbase and other Exchanges are not supposed to facilitate the transfer of funds for gambling.
And are supposed to try and police their users from doing that.
As time has passed and US licensed sportsbooks started appearing the exchanges appear to have been putting a lot less effort into this area, but still will ask users to stop using them if they end up with information they cannot ignore.
The easiest way to 95% avoid the chance of this ever being a problem is to simply respect those terms enough to not completely ignore them by transferring funds directly to/from a Coinbase wallet to a sportsbook.
Always transferring to your own personal wallet in between Coinbase and Gambling sites is the smart way to handle your crypto transfers. Often this is called using a Middleman Wallet.
This also means that if anything ever goes wrong, you are personally at one end of every transfer, enhancing your ability to see what is going on and not having to rely on two third parties to liase to solve a problem.
Anyway, none of that really addresses the question. Or the reason why the question comes up so often.
Whenever using a Middleman Wallet is mentioned, someone will usually pop up and say "But how would they ever know I was sending money to a bookmaker anyway?"
The main way exchanges track what users are doing with their funds is via Blockchain Analysis tools like Chainanalysis . One way they identify which wallets are connected is by tracking change and dust in wallets. They look at usage patterns and can reliably identify if you are a trader, investor, merchant (or user of merchants), an exchange, a bookmaker and most importantly to them, if you are doing anything to hide your tracks which might indicate money laundering. Another way they come up with wallet addresses used by bookmakers is when they ask users what their activity is and are told I am sending to XYZ bookmaker.
Once they have info that a wallet is owned by a bookmaker, the simplest first step is to check if any of their users have sent directly to any address their analysis has shown is controlled by the bookmaker via the wallet info they have.
It becomes exponentially more time/power consuming to start checking steps further than a direct transfer. That is why in most cases using a Middleman Wallet will avoid you ever being flagged.
Of course, if Coinbase had some reason to look specifically at just your account, it would be simple for them to trace every step every piece of Bitcoin you have ever owned has come from and gone to. But that is highly unlikely to ever happen if you never use a Bitcoin mixer or any other method of hiding your bitcoin tracks that is common in money laundering.
Long story short. 1) try to respect your exchange's terms by not sending direct to a bookmaker from their wallet and 2) don't act like you are doing anything wrong. If you are not doing anything wrong, do you really need to obfuscate your crypto tracks?