StingingVelvet: Private companies can do what they want. Google could announce to the world they're banning all "Conservative" content if they wanted to, and that would be fine. Conservatives would then be free to stop using it, and rush back to Yahoo or whoever else. That's freedom baby.
A lot of today's "Conservatives" are far from Conservative on this issue lately though, sadly.
While I normally agree that private companies are protected by the First Amendment - there are exceptions as freedom of speech isn't absolute. For one Google is protected from lawsuits by laws treating various online platforms as public squares. The problem is that if you ban certain speech the square really isn't public is it?
The reach and power of Google create anothe dilemma. Monopolies and oligopolies pose an issue. If Google bans you - okay fine, if Google, Twitter, Instagram, Facebook, Apple etc all ban you then there's a problem (and if they all ban you one after another - then you have evidence of a cartel). Furthermore should some of the services Google provides be considered utilities? Is Google's reach be that tremendous? Could be - landlines are considered utilities and they aren't as popular as Google is right now. Utilities can't deny service except in some very specific circumstances such as non-payment (and even then they can't do so absolutely).
Of course this is all secondary to the idea that Google seems to want to supplant the government. A private corporation controlling the goverment should be the last thing anyone wants (the government has checks and balances - a corporation does not). I like playing Shadowrun - I don't want to actually live it. I like politics out of my games, but I also want my games out of my politics thank you very much.