I wonder if it'd be possible to fix a lot of these issues by having a constitution with damn near impossibly strict standards for changing it that rely on the entire population agreeing (or close to it)?

So there might be a right to privacy or freedom of speech enshrined in law, and the only way to change it would be for 90+% of the population to agree to change it. That way, it'd only take a minority disagreeing with a bad law to make it impossible to pass said law. Reactionaries and extremists would basically be defanged entirely, since they'd have to get most of their opponents to agree with any changes they propose, not just their own followers.