There's nothing unlibertarian about a private business making up its own terms of services and privately enforcing them. That's exactly how the free market self regulates without the use of force.
When a single business dominates an entire industry in such a way, it's not just a "private business" anymore - it's an institution and should be treated as such.
I must admit that it's amusing to see libertarians complaining about the decisions made by a private business and implying that the government should step in.
This reminds me of an op-ed in my private college's newspaper written by a self-described libertarian that using a portion of tuition to create a scholarship fund was a socialist redistribution of wealth.