I have built up a "trusted" network of friends for these Peer-to-peer trades over time and I can even trade with them, without using escrow services, but newbies will unfortunately not have that privilege.
Yes, there are definitely shadier alternatives that I'd rather not use, but people may be forced into using. A lot of current casual buyers/sellers may also have to turn to centralised exchanger services with no escrow protection, which is a big concern.
For whoever that doesn't know yet, Localbitcoins gave out an entirely new and updated terms and conditions a few days back as well: https://localbitcoins.com/gdpr
These restrictions don't really affect newbies yet, though. They still have a chance to trade without significant volume. Although key word is *yet*. We don't know if Localbitcoins is going to follow current guidelines forever.