Thanks to everybody who replied. My feeling is "often". DMs are a technology that allows people to have confidential conversations if they agree to it. There are some tacit indicators that show that I want this discussion to be confidential, like sharing something personal or including personally-identifying information. But it is a negotiation, not an intrinsic contract.
You can't use DMs to bully people, and then get mad that they share the DMs. Unless they agreed to confidentiality with you, there is no problem with sharing your DMs. If you feel like there was a tacit agreement and they betrayed your confidence, get better at negotiating next time.
It is nice to ask if you want to share something with others, but not required. Don't commit to confidentiality if you don't trust the other person or people.
This is like physical in-person communications. If you are going to tell someone a secret, get their assent first. Being explicit is your safest bet and very much appreciated by all other communicating beings.
@evan I agree. I think my answer of "often" also comes from a place of having been a bit of a microcelebrity back on Twitter, where I got loads of DMs from strangers. If you're cold DMing someone, that person has no obligation (in most cases) to keep that communication private.
@evan That said, there are times when strangers have DM'd me when I felt obligated to keep what they said confidential, like people who thought they might be trans, people who've told me that they were abused or assaulted by someone I knew, or people who misread my name and thought I was a rabbi.
@evan Personally I view it the other way round: a DM is confidential unless you both agree otherwise. It’s like email sent from a friend or acquaintance: I wouldn’t share a personal email to me unless I got the other person’s ok. That’s just how I see it (fwiw I voted ‘never’, but probably ‘rarely’ would’ve been better).
@evan It's not! It didn't even occur to me until I had a very awkward conversation with someone who, it transpired, had misread my name as "Rabbi Cohen".
@ricmac I think also when someone has a story under embargo, they need to specify it in the email, and usually get your buy-in before sharing the information, right?