Yes they are private, and of course, they are free to choose there own customer.
On the other side, as long 8chan did nothing illegal, they shouldn't shutdown 8chan. If 8chan did something illegal, then for this we have the whole justice system.
If people think 8chan does something bad, but is not illegal .. then people should vote to change the law.
If private company's start to play the police .. it does end in a disaster. Special since today's web is a winner takes it all model. If you felt out of Youtube .. yeah, just bad for you. Apple credit card .. yeah, you can buy just almost everything .. yeah, bright future ..