No, it's not. There's a world of difference between running your own website, and running a site on hardware owned by someone else, managed by a completely different party.

Now if it were the ISPs handing this ruling we'd be on the same page, but it isn't. There's no freedom of speech argument for "right to demand services without restriction". Same way a restaurant will turn you away if you show up with "no shirt, no shoes". Namecheap is using the freedom of speech of it's leadership in saying "Nazis and other groups that incite violence are not groups we want to host".

Seems like a distinction without a difference. Even if you run a website on your own server, you are still using the ISP's hardware, so they could make the exact same argument. And hosting services are so popular exactly because ISPs have discouraged self-hosting.

Right for service totally without restrictions, no, but "viewpoint-based discrimination" or other types of discrimination are a separate legal category for a reason. "Shirts and shoes required" is different from "whites only" (or, for that matter, "liberals only") on a restaurant door. We allow the former but not the latter, and I think that's reasonable.