A never-ending argument
Supporters of the site and/or free speech argue that activism of the sort practised by The Lawyers' Committee for Civil Rights Under Law is a restriction on free speech. Others point out that GoDaddy is a business, not a government, so has every right to decide how its service is used. Others still say the likes of altright.com are so far beyond civil speech that they deserve censure
A very succinct summary of the different points of view.
And the validity of each argument depends on the situation. As has been frequently pointed out, 'free speech' does not allow people to say anything they like, in any situation, and not expect consequences. By all means you can shout 'Fire' in a crowded cinema, but expect to spend the rest of your life in jail for causing numerous deaths in the panic.
In this case, the second point applies. Individuals and groups have a right to decline to facilitate speech and actions they disagree with. I must admit I'm not comfortable with the decision about declining to bake a cake for a gay marriage being illegal. An unpleasant manifestation of a closed mind, perhaps, worthy of censure, and boycott of the business, but not actually illegal. Would I be acting illegally if I declined to build a new website for the alt-right, or the 'Welsh' Labour Party? Of course not. So what's the difference.
In this case this is exactly what Go-Daddy are doing. They are merely declining to facilitate alt-right. It might be different if it was a notional public monopoly, such as ICANN, refused to allow them to have a domain. But where that domain is hosted is a different matter. If necessary they can host a site on a laptop in their shed, if they can find someone to provide a fibre connection. If they have enough dosh let them set up a hosting provider exclusively for really unpleasant scum sites. That's their right, so long as they stay legal, and don't incite hatred and violence.
So, thumbs up to Go-Daddy (for once - not the best of hosting companies!)