If you open your account on centralized exchanges, you must read Term of service and follow their guides. If you break ToS, your account will be under investigation of Compliance team. They might suspend or restrict your account.

Mixers are not good because exchanges are keen on being strict with mixers. They don't want to get troubles with governments and money laundering. You can mix your coins with mixers if you want, after you buy your coins on exchanges, and withdraw it to your non-custodial wallet. After that, you can send your coins to your non custodial wallets to mixers.

If it is Bitcoin, you can use Wasabi wallet and Coin Join transactions. https://wasabiwallet.io/
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