This sounds to me like a compelling case for parental anonymity online. When you write publicly about your children under your real name, anything you say can be found when some searches your child's parent's name.
If you shared each individual negative story under a new pseudonym, and each account shared only enough detail to clarify the story while leaving great ambiguity about which family it's from, the reputational risks to your children would basically vanish.
This seems to work as long as each new account is sufficiently un-findable from your real name, for whatever threshhold of findability you deem appropriate.
Yeah, I can second this entire sentiment. I try to write up parenting tricks that work for me that are clearly not going to reflect negatively on my kids, or will even feel too personal. And then I realized that a lot of the most valuable information that I could read as a parent, I'll never find cause a parent with high integrity is not going to write down very negative experiences they had with their kids and all the ways they failed to respond optimally. It reminds me a little of Duncan's social dark matter concept.
In general I'd like to see a lot more of people writing about their failures in addition to their successes. If a bunch of people all try a thing and have mixed results, and only the people with good results write about it, people who don't know about this selection bias or don't realize its extent are going to end up with overly positive views. I've written about some of my mistakes, and I think it would be good if this were a higher fraction of my posts.
On the other hand, once other people are involved this isn't entirely up to me. One place this comes up a lot is parenting: I don't want to write things about my kids that they don't (or won't) want public. This is especially tricky if I write a post about something we've tried which worked well in part because the kids did a good job with it, and then later they stop doing a good job.
I don't have a good solution here. I don't want to go all the way to "if this had come out with my kids looking bad I wouldn't write about it, so I also won't write about it if they look good" because this would exclude a huge fraction of things involving the kids (there are a tremendous number of possible ways kids could do something that would be embarrassing). Sometimes I can handle it with plausible deniability (one of our kids did embarrassing thing X) but often it would be clear to some people which kid actually did it, or it's bad enough that even being in a pool of three is mortifying. Other times I'm able to include some minor negative information, if it's about them when they were enough younger and it's combined with positive information. But mostly I think this will just need to be something people keep in mind when reading my posts, and posts by other parents.
I asked one of my kids what they thought about this issue and they suggested: "only write about things where [sibling] looks bad and I look good, such as [redacted]".