If the people had their way, those suspected of child sex crimes wouldn’t even get trials. Things like privacy and due process only exist to the extent that a ruling class has the power to impose their own values, contrary to popular will.
These cases of people actually claiming to want people locked up without due process are pushed by a vocal minority (same with us - even hacker news posts with maybe a million views mean than 1% of U.S. adults read it) - almost everyone wants due process since we want the truth to come out in the most verifiable way, and the court system provides that, even if it involves humans that can be bribed, persuaded, and manipulated by rich & powerful people.
This made me come up with a thought experiment. If you sampled a thousand parents and asked them if they think sex offenders deserve a fair and just trial, what do you think the result would be?
That question is framed wrong. What you should be asking is "Should people accused of such crimes get a fair and just trial?". This makes it clear that it takes me one sentence to put you in that very position. And that's exactly the problem. Your formulation erases any question of guilt, which makes the discussion nearly impossible to win for the privacy side.