This already happened a few times, actually in the US. Nonetheless, that's a rea issue. Stop using damn mainstream messaging apps and start using privacy orientesd ones like Simplex and XMPP protocol
Discussion
The issue with XMPP based messenging will be: XMPP needs servers just like email does. So the authorities will just eventually force bigger XMPP server hosters to either (A) implement "some way to achieve chat control features" (which seems rather impossible protocol wise) or (B) shut down. So they might just have to shut down.
Might push people to mostly serverless messengers such as https://briarproject.org or https://tox.chat.
Or maybe since they cannot easily force shut down of email servers, people will use Delta Chat, which uses emails? Email providers wouldn't like this though.
Forgot to mention Jami (https://jami.net) which is also p2p.