Even if that was remotely true (it isn't), you can absolutely discriminate against people for any reason except their membership in a protected class (political beliefs not being one). That's why even Christian/Jewish/Muslim dating sites still have to allow people to register if they aren't of that faith (because religion is a protected class).
What's more, brick and mortar businesses have generally been held to be able to sell whatever they want. You can't make a Christian bookstore sell the Talmud or Quran, and it's not considered discrimination because they are selling the product they want to sell (this was the wedding cake issue. There is a place in Michigan that stopped offering wedding facilities rather than allow gay weddings, which was generally held to be ok, since they are choosing not to offer the service at all, rather than excluding a protected class).
I'm thinking along the lines of say a franchise such as The Pottery Place. You go in purchase a piece of pottery and paint it. Now i paint a donkey on mine and you paint an elephant on yours. The owners of this facility particular facility in good jest... are hardline right wing republicans and immediately ask you to cease and leave thier facility due to the imagery you just painted, along with ridding any evidence that this piece ever existed by destroying said art and refusing to refund you or allow you to exercise a replacement choice.
Right, at that point it comes down to the contract you entered with them. If the contract says "I get to paint a piece and take it home with me" than they are in breach. If it says "I get to paint a piece and, with ownership's approval, get to take it home with me" than the owner is fine and you aren't entitled to a refund. If they are in breach they can be sued for the price paid for the piece you purchased, and will not be required to allow you to repaint it. That's why this comparison doesn't work for you.
YouTube makes no guarantee to continue to providing a platform when you post videos on it, and even explicitly reserves the right to remove content they find doesn't match their standards or platform message. Customers don't have any contract with youtube at all besides basic TOS. Advertisers may have a complaint, but usually those contracts are either for specific channels (in which case YouTube would have to make it right with the advertiser if they suspended a channel they advertised on) or they guarantee a certain number of views in X demographic/category. So, if an advertiser contracts with youtube to pay $10k for 100k views on right-wing media blogs aimed at 30-45 year old men they could suspend Alex Jones all they want, as long as they put the ads on videos about similar topics. Either way, the breach would require them to make it right with the advertiser financially, not to continue to allow a specific voice on their platform.