Re. the issue of whether the "we believe you" campaign would leave people unfit for jury service. For me, at any rate, it's an issue of what your prior belief set is and how you update it in the light of evidence.
(Bayesian theories of belief point out that everyone starts out with an initial set of prior likelihoods - probabilities - that they adjust in the light of further evidence. For instance, if you were betting on a horse race, and had no evidence other than that there were five horses in the field, you might start out by giving all of them a probability of 20% of winning. Then if someone told you Lightning Flash had won its last 4 races, while Three Legged Nag had fallen at the first in its last 4 races, you might up your assessment of LF's chances to 50% and downgrade TLN's chances to 1%).
So that's what I'd do in a rape case - I'd start from the belief (based on my understanding of Home Office and Police Stats) that only about 5% of rape accusations are maliciously false. I'd also factor in the chance that it was a genuine misunderstanding - she didn't consent, but he genuinely thought she did (so rape from her personal perspective, but not rape in the eyes of the law). Then I'd listen to the evidence.
And in this respect I'd be no different from anyone else - because we all go into situations with a set of prior probabilities (even if we've never thought them through explicitly). So someone who's experienced a relative or friend being falsely accused might quite understandably start with a prior where they believed the rate of false accusations to be higher than 5%.
But regardless of our priors, I trust that we'd both take jury service very seriously - and I'd be prepared to acquit if there was insufficient evidence to prove guilt beyond all reasonable doubt, and the person who'd come across cases of false accusation in the past would be prepared to convict if the evidence dispelled all reasonable doubt.
The bottom line is no one comes to jury service in a vacuum - we all have prior beliefs which may be correct, may be erroneous. But the jury system rests on (I think) three principles: (1) the jurors are decent people who really want to get to the most truthful outcome they can; (2) that it's better to live in a society where the occasional (or even quite a few) guilty person walks than one where innocent people are routinely convicted; (3) not guilty can mean "innocent" or can mean "we weren't convinced beyond reasonable doubt", and because on the basis of newspaper reports none of us outside the jury room can know which is the case, you should not be pillorying either the accused ("they got away with murder") or the plaintiff("they should be tried for perjury for making false accusations").