The real risk is which trader we are dealing with because p2p exchanges filled with scammers who will send real money but from a hacked bank account so whoever dealing p2p should make sure the funds are coming from the owner not from third party that is where the again identify will be broken.
Exactly. The risk is in this case that you sell to a scammer which has stolen an account and later the legitimate owner of the bank account reports the trade to the authorities, which can get your bank account frozen and you'll be charged for money laundering and fraud. This has happened to several Bitcointalk forum members.
Regarding risks, there are however big differences between a fiat -> Bitcoin operation and a Bitcoin -> fiat operation.
For a fiat -> Bitcoin operation P2P services like Bisq you generally do not put your bank account at risk (the only case being that you're transferring money to a stolen account a scammer uses for money landering purposes, but that's not very frequent). The risk is here that in theory your counterparty could allege they haven't received your bank wire. However this is mitigated by the security deposit Bisq requires, like BrianH has already wrote, so I would consider this operation of relatively low risk. At least the scammer can't win anything in this case, only lose.
But a P2P/Bisq Bitcoin -> fiat operation is highly risky. Not only because of the risk for your bank account as I wrote above, but also because scamming "this way around" faking proof for the escrower is at least a little bit easier. That's why for Bitcoin -> fiat I recommend indirect methods like those I mentioned in
this post. Or buy the things you need for your everyday life directly with Bitcoin if there are shops accepting it in your region.