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".
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".