Starting with the game theory:
If the TCR shows a specific bias (ie: political inclination) or some form of censorship, less people will want to own the token because the "fairness" promise is broken and that should reduce the token price.
If the curated items (newsrooms in this case) have low adoption (few people use tokens to purchase viewing rights) then the tokens will lose value too.
For token holders this should motivate them to be judicious in their curation efforts.
The voting mechanism also plays a significant part on the whole system. Traditional TCRs use a partial lock commit reveal scheme that allows us to find the Schelling point for a challenge.
Personally I'm quite partial to other voting systems that reduce the impact of token ownership disparity like the one Glen Weyl, Buterin and others have called "Liberal Radical" and its simpler root the quadratic voting mechanism. The way this works is that only the square root of voter's balance counts as voter's voting "weight". So 1 vote costs 1 token but 2 votes cost 4 tokens and those with less "power" have a higher representation relative to their balances.
I don't think the voting mechanism is the problem. The problem is the humans who vote. For example, let's say that Civil attracts 10 publications to its platform, all of which are liberal leaning (which seems to be the case). So, when a conservative newsroom wants to join, what do you think will happen?
The Civil Constitution [1] has no guarantee of freedom of speech. Instead they say they are "committed to the ethical practice of journalism," which is open to be arbitrarily abused by the majority of voters, irrespective of the voting system.
I don't actually understand why there is any voting at all.
The author of the original article says he believes that Civil's leadership has 'good intentions" but if they can't understand that their system will not solve the problems they set out to solve, then perhaps they don't deserve to gain the funding and attention they have actually managed to get.
What I think will happen is that voters are incentivised to make good on the promise of the platform. If they reject a conservative site based on anything dubious then the whole effort will lose credibility.
Don't forget that some form of voting is necessary for the token holders to have a say in the governance of the business. That's one of the premise of blockchain native businesses, the decentralisation of equity and power.
The voting and incentive mechanisms are the cryptoeconomic properties of the project and what I can discuss intelligently. The Civil constitution is out of my scope but I trust the incentives are there to allow high quality media to enter the list regardless of political bias.
This just leads to censorship by the most powerful users in the system.