Why is that not okay? Do you think that is sensitive private information? Or do you believe that no content of any private conversation should ever be publicized?

They could be privately supportive of Black Lives Matter, donate to bail funds, spread the word under anonymized accounts, etc. But they might also work/live in a deeply conservative office/neighborhood. Forcing their hand at going public with their support could get them fired, or get their ass kicked the next time they go to the bar or get pulled over by a cop.

And "find another job, then" isn't always practical, especially with marriage+kids+debt.

And yes, you should always ask for consent before making a private reply public.

I'm supportive of Black Lives Matter, but I don't think what OP did was ok.

> They could be privately supportive of Black Lives Matter...

Of course they could. This person didn't claim anything to the contrary. The complaint was not about the webmaster's personal beliefs, but rather about the webmaster's decision in their capacity as webmaster.

> Forcing their hand at going public with their support could get them fired

The request was to change the website of an open source project, not for the webmaster to personally declare anything about their beliefs. Of course it is possible (though unlikely) that there is some threat to the webmaster's safety or livelihood that would prevent them from taking certain actions regarding the project's website, but in that case, the responsibility over the project's website should probably be more evenly distributed.