Bisq is currently a prime example of how you don’t need to identify users to provide good security.
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Best we can do here is do two things. First is that Bisq requires that the sender provides the name of the account that will be sending money in Bisq, this makes it harder for a buyer as he needs to know this information from that third party. Secondly account age witness provides trade limits for new accounts. Buyer would have to wait a month to double his limit and two months to double it again. This waiting period exposes higher risk for the buyer to get caught if he is doing something illegal.
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Bisq doesn’t identify buyers. I am not sure to which problems you are referring to, but Bisq has generally small trade limits that makes it undesirable for most criminals. Currently traders experienced no issues with any money laundering problems.