I'm not posting this in agreement. Or not full agreement, anyway. It's been posted and shared on my feed in facebook. As a general principle: Absolutely. Your opinion about my experience is not as valid as my experience... usually.
The problem is that I'm a social scientist. That word "opinion" is carrying a lot of weight. If someone's ideas of what a non-lived experience is like are based on supposition, best guesses, and their own experience, then the graphic is valid: lived experience is much better.
However, if an "opinion" about my lived experience comes from the reported lived experiences from relatively representative thousand or so people, the opinion is probably more valid, for certain purposes/contexts.
"Validity" always has a context or target. No matter how much amazing research I have about a certain issue, my knowledge is never as good for an individual as that individual's lived experience. However, if "valid" means "generalizably true across lots of individuals," then one person's experience will never be as valid as a reasonable (lots of weight on that word) summation of many others' experiences. Another detail is whether one's interpretation of one's experiences (especially interpretation of causality) is necessarily more valid than interpretations by others who haven't lived the experience.
If you're feeling uncomfortable about this analysis, consider a parent whose child develops autism. The parent is fully convinced their kid's age 2 vaccinations were the cause. That parent has definitely had an experience, which included seeing their kid vaccinated, then seeing autism symptoms emerge. None of that means the parent's interpretation of that experience is accurate. No, the vaccines did not cause the autism, but try telling the parent that. They might tell you that they lived the experience so their interpretation is right.
And they're still wrong. Yes, the experiences they had are theirs and valid and valuable. That doesn't mean nobody else can have a more valid opinion about their experience--specifically, a more valid opinion about the causes of their child's autism.
This dynamic applies in many areas of our world: are soldiers' views of American foreign policy always more valid than non-soldiers" views? The soldiers lived the foreign policy experience, after all. Are a patient's views of their disease/diagnosis/disorder etc. always more valid than the views of medical professionals? The patient lives the experience, right?
In plenty of domains and applications one's lived experience should not be questioned by those who didn't live it. I'd say this should be the default in living our lives (hence my lack of concern about this meme even though I don't quite agree with it). However, the vague use of terms in messages like this might contribute to a belief, as Asimov said, that "my ignorance is just as good as your knowledge" (not Sagan; thanks, @courtcan) fueled by the insistence that one's interpretations of one's experiences are superior to all other interpretations.