I'm addressing what you said, in a succinct way. If it's a little too unclear, then:
The real underlying question is ‘are those that violate social contacts due the protections of said social contracts’?
No, they're not. But, you have no idea who has violated the social contract unless you have due process.
Those that you're not sure yet have violated the social contract, because it hasn't been proven, are due the protections of said social contracts. Yes. That's the trial phase. Then, after that, we decide they might not be due the protection of the same social contract. That's the punishment phase. They're different. It is extremely popular in times of crisis to start to skip ahead to punishment without trial, as part of the official process, because things are so dire, and that's explicitly what this person was advocating for. That is wrong. Because you'll wind up punishing people who haven't violated any social contract at all.
Are we still bound by the rules of a contract that another party actively violated, in regards to that party?
No. But once it gets to a broad scale, and due process breaks down on all sides as people start a big melee for their own safety against their enemies, things can get very very bad.
Sometimes there's no way around that, of course. That's what we call a war. Maybe that's where we are headed. But deciding ahead of time that you're going to abandon due process within a civil society, because of how dangerous it is that your opponents want to abandon due process, is just hastening the phase of "might makes right." It's pretty hard to come back from that once it happens. A lot of people have had to grapple with this, notably the allies after World War 2 trying to figure out how to punish the guilty. If they'd gone with this "they're SO bad that they don't deserve due process" type of thing, Oskar Schindler would probably be dead.
If you answer yes, this leads to the ‘paradox of tolerance.’
No. Not having the trial and doing nothing, or having the trial and then not doing the punishment, is tolerance. Having the trial and then punishing is justice. Not having the trial and doing the punishment anyway is terror. I'm not aware of a time when that was the solution that didn't go horribly sideways almost instantly.
There are times when there was some massive crime against humanity and the paradox of tolerance prevented effective resolution, and it was very bad. Reconstruction is a good example. But just doing arbitrary punishment for anyone some random person decides is guilty is ten times worse. Even if you get it right 100% of the time, which you won't, it sets a precedent that is horrifyingly hard to stop once people have gotten in the habit.
Seems a little more clear spelled out that way?