The legal requirements are still being delineated but it is already clear that it will bring major changes into the functioning of virtual currency exchanges. The most important changes concerning LocalBitcoins’ users will be related to improving the registration of new accounts and the identity verification processes, introducing wallet withdrawal and trade volume-based verification tiers.
We will keep you informed through blog and social media updates and will provide more detailed information on the coming changes during March 2019.
https://localbitcoins.com/blog/aml-regulations-compliance/
Perhaps other similar peer to peer methods are going to develop? Paxful and others?