Well, yes and no.
The theory is that government, as the agent of the governed, promotes ideals the governed wish to see established. There may be a tension between some of those ideals, such as free speech and the expression of views the majority of the governed may find odious. Corporations may be forced to put up with things they find objectionable, such as paying for employee health care plans that offer contraceptive services. In this case GoDaddy can say they're booting The Daily Stormer because their speech is odious, but they're really doing it for economic reasons.
(And that's OK! Economic pressure is a legitimate means of driving change. In this case the form of the victory is enough, even if its substance can be questioned.)
But a corporation's scope for censoring speech is limited by the norms society imposes, whether de jure or de facto. If it were so inclined GoDaddy might have a hard time booting a site promoting marriage equality because that's a norm a majority of the governed want to promote.
What I'm saying is that GoDaddy is right because you and I both agree with the result (so it pleases us), but it might also be right to allow the site to remain because these idiots have a right to their hateful opinions (so it satisfies our societal norm regarding free speech).