(And there are the second/third order negatives of Psionics that probably only Utau knows for sure:
Passive, consistent and unfiltered Empathy projection may make those around her unable to fully recognise/navigate their own emotions by themselves [too much extra input, or mild 'jumping on "problems" before they truly become apparent/have had time to try and navigate it by themselves'],
or view interactions with non-Psionics less positively due to it being less 'real' [since it's impossible to people to be this 'real' normally, not even the most outgoing or transparent people without Psionics],
or simply having a much harder time recognising non-intense emotions and/or interact with other people in a black-box manner that non-Psionics usually do,
or...)
The biggest problem here really is that Amu/Utau are the only ones to really have the perspective to get through to Ami like this, but Amu doesn't fully understand yet (or understand just
how integrated Psionics are to Ami's worldview, or even know it's important to try and find out), and I cannot see a story path that makes narrative sense for Utau to have said conversation with Ami at all.
Approach that in the wrong way, and they'll all be seen as a real life version of The Omen.
Basically, these are teething first-generation Psionics problems, not helped* by the formative years being kept a secret by Tsukasa** or something?
And as for how well this turns out, the ball is in our court now (and also in the court of the media - hopefully they actually think more before they post what they post) :/
* Not that Tsukasa exposing these things earlier would have helped much: As you mentioned, Amu's parents being so accepting isn't exactly the average - you don't need to be a bad parent to have difficulties with these things; and the really troubled ones might then encourage their children to use Psionics in negative directions!
Besides,
without Tsukasa spending effort to at least try and gather Psionic users in one place, it's much harder to establish a set of norms for ability usage, or to slowly teach them the results of misusing [for a given value of the word] Psionics via pushback from fellow Psionics (exhibit A: Saaya); and given that there are non Psionic users in this school this also tries to avoid the perception of there being an inherent divide between Psionics and non-Psionics.
Furthermore, Tsukasa does
not have access to mind shields because he's not part of the government - he's only had so much he could do, and I think overall even with the flaws, edge cases and potential blowing up he's done a very good job with what he had.
** As far as I can tell, Psionics is an inevitable result of Overgrowth, Overgrowth is an inevitable result of the Collective Unconscious being very big, or whatever actually happened back then in this setting; and the Chara system is a restraining bolt on Psionics to allow it to be used in more positive directions (or not be used at all without Charas, period)