While DMs on fedi are not secure, there are many safer alternatives for private or sensitive communication out there. Here is a curated list of @em's favorites:
Matrix is a secure messaging platform similar in design to Discord, but which utilizes End-To-End Encryption (E2EE) in DMs and other encrypted rooms. The most popular Matrix client is Element, but there are many clients to choose from.
It is strongly recommended to sign up with an alternate homeserver (i.e. not matrix.org). A good choice right now is cuteness-overdose.com.
SimpleX Chat is a secure messaging platform that may be simpler to get started with than Matrix. You can download the apps from their website.
Tor is an anonymizing network which provides safer access to most sites on the internet.
Tor Browser is the simplest way to access Tor. You can download it on their website.
Tails is a bootable image that provides more complete anonimization through the Tor network. You can download it on their website.
Excavator is a Tor hidden service search engine. It is located at this .onion address (requires Tor to access).
Tordex is a Tor hidden service search engine. It is located at this .onion address (requires Tor to access).