Popa, the rabbonim do have ample opportunity to tell the difference (sincerity vs. insincerity). Their signing off on the giyur indicates that they found the geirim sincere. The trouble starts afterwards — when uninvolved Jews, citing media reports or the omniscient “everyone knows,” treat geirim singly and collectively as insincere or under suspicion.
As for those who find geirim weird and therefore fit for hands-off treatment, I don’t think there’s a non-weirdness test that geirim have to pass before, and kal va-homer after, their giyur.
It’s not an academic issue. I know several geirim who have been wonderful frum Jews for decades who now live in fear that someone whom they’ve never met, let’s say a certain dayan, is going to put their lives (and those of their children!) under a cloud of suspicion.