I guess I'd question your fundamental premise. Would a pharmacological treatment be accepted if all the trials showing its efficacy were unblinded and the important outcomes were only subjective? I don't think so. So, why would that be acceptable with other sorts of treatments? Requiring good science doesn't seem like a radical stance. Are you suggesting that we should find a way for the GET trials to be dismissed that will leave the findings of other reviews with the unblinded trial/subjective outcomes problem unaffected - reviews that probably also have seriously negative consequences for people?
Yes, the specifics of a disease can make things complicated; just requiring that there be an objective outcome isn't enough. I've mentioned before that scientists and advocacy groups working on particular illnesses might choose to get together and make an explicit list of outcomes that any treatment study should include. For example, for anorexia nervosa, the objective outcome of weight is not sufficient in determining treatment success if only measured immediately after treatment - anorexia nervosa researchers have called for outcome standards for research that include longer term followup. For ME/CFS, an objective outcome of activity monitored for only a week after a treatment ended would be hopelessly inadequate.
In the absence of an agreed illness-specific standard for core outcomes, Cochrane needs to clearly state what outcomes its reviewers have judged as indicative of treatment trials meeting basic standards. If Cochrane sincerely thinks that unblinded trials with subjective outcomes are totally fine when assessing trials for a particular illness, then it needs to state that upfront in its reviews. And then everyone can draw their own conclusions about the quality of the review and the reviewers, and the utility of the Cochrane brand.