As per current enforcement of the back-it-up policy, we require answers to either list references or explain how personal experience is relevant in the answer. This should improve overall quality of the answers, because you can understand the context of how and when this answer applies.
Now, as Interpersonal matters go, some can become quite personal.
For example from the last weeks I recall: sex, divorce, polygamous relationships, father<->son conflict, death of a loved one etc...
Now I see a little conflict here as not everyone who has relevant experience may want to discuss that openly on the internet. On the other hand, answers from a well matching personal experience can be more valuable then some conjured links paired with a random suggestion. So it could be detrimental to the overall quality of answers one gets if we require too much detail to back up exactly which, how and why the answered can relate.
How can we maintain the balance between backup and and privacy?
Edit: First, I have no clear opinion on that topic but rather see a optimization problem I´d like to see some opinions and ideas on.
Second, I´d like to remind that this whole Stack-exchange system is really built around finding that one brilliant answer, not about getting enough answers. So there will always be a trade off to be made between being open to contributions and weeding out the low quality answers by raising the bar for answering in the first place.
How best to shape that trade-off for those especially delicate topics, is what I want to discuss - a problem that most other sites don´t seem to have, because the are just not that personal! Ideas to mitigate that problem entirely are also welcome (like option 2 of @Em C´s answer)
For reference I´ll include a piece of the co-founder: Optimizing For Pearls, Not Sand