its not just that google has a search engine, they also own youtube, which plays a huge role into how people are getting their news today, as people watch less and less television.
bobdole123456's point is that monopolies aren't illegal but abuse of monopoly power is illegal (you're being downvoted because you do not explicitly address that fact).
But I actually think you raise an extremely interesting question: does pushing a political agenda using your monopoly position constitute an abuse of monopoly power?
The advent of privately controlled monopolistic forums is somewhat new. I don't think it's at all obvious how the spirit of anti-trust law should be extended in the age of platforms...