A mix of fear (of what they don't understand) and envy (of the power psions can wield). Everyone will have a third-hand story of someone whose mind was scrambled by a psion, and most of those story will be fakes. We had witch hunts in the past, psion-hunts are the same.
You are right that the seeds of Suppressions where already there back in the millieu zero, and probably had always been present.
Or I'm just overly pessimistic.
Just map the experience of being psionic to that of being LGBTQIA+ in the Sixties. It was illegal in the UK, right up to 1967 when the Wolfenden Report broke the hysteria apart and took homosexuality off the statute books.
It took thirteen more years for the World Health Organisation to take being gay off their list of dangerous communicable diseases. Seriously. They used to think that being queer* was catching.
Then Thatcher came along with Clause 28, which became Section 28, and being gay was a crime yet again. Took fifteen years for that stain to be scrubbed out of the law books.
Now map that to the psion experience. Psions hang around with one another, form secretive communities, seek relationships and to raise families with their own. And then you get the karens out there who think it's catching, and psions hang around bathrooms looking to turn kids into telepaths.
That's the look of the dumpster fire, right there. That's the subtext. Whether you like psionics in Traveller or not, they're a persecuted minority, and the parallels with being LGBTQIA+ in the late 20th century, where Traveller was born, are inextricable.
Point being, psionics is part of the character's identity, as much as being an Aslan or a Vargr. It isn't like a career - you can be a former Rogue, an ex-Army grunt, and of course there is always retirement, even for Marines (gawd bless 'em) and Scouts.
But you'll always be a psion, possibly as alien as any weird creature sitting at your Free Trader's Navigation console.
*Present company included. I've been the B and A in LGBTQIA+ since childhood.