> I’m not seeing the connection here between “antitrust” and the alleged discrimination against conservative views. How does alleged discrimination become an antitrust issue
Discrimination regarding expression and ideology/belief becomes an anti-trust issue when you're dealing with platforms, broadcasters, or otherwise distribution systems in cases where the company has a monopoly.
The NY Times and Fox News may discriminate on the basis of political ideology, precisely because they do not have a monopoly on news. If one of them were the monopoly, it would be acting as a censorship extension of the US Government so long as it were allowed to keep that position. The actions of the monopoly would be the actions of a government censoring speech and expression by extension.
Why? Because there is no alternative. At that point it's not merely a company with a bias, it's censorship.
The government is given power to deal with monopolies, via anti-trust laws among countless other agency controls. They're often the only entity powerful enough to be capable of removing a monopoly (consumers realistically can't get rid of eg cable or airline monopolies without the assistance of the government).
Google and Facebook both have monopolies directly dealing with expression and distribution of information.
Facebook's social monopoly is a multi-faceted monopoly that is extremely entrenched. Its actions to block speech are de facto censorship accordingly. In the course of censoring, it's inherently discriminating. It matters because they're the giant monopoly in social, with WhatsApp, FB, Instagram.
Google has a global monopoly in a distribution platform (Android), a search engine monopoly, and YouTube (a broadcast and distribution platform). There are no serious, large competitors for what YouTube does, it's overwhelmingly dominant. Its monopoly in that segment of video is every bit as strong as its search engine monopoly.
If Google, using its search engine monopoly, decides to remove all/most search results for the left or right politically, then it's a clear anti-trust abuse (to use a glaring example). It's using its monopoly position to censor. Only the government can deal with monopoly abuse with any consequential immediacy. For example in a case where a monopoly like Google or Facebook attempts to throw an election by using its monopoly power.