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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.
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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.