Obviously some images are more harmful and illegal than others, but Namecheap has absolutely no business acting as judge, jury, and executioner when it comes to something that in no way passes through any part of their infrastructure.
If they’re not hosting the DNS or web servers hosting the offending image then they should stand down. They took down Imgur for not deleting an image within I believe it was 2 hours of notice. Completely unprofessional.
I'm not sure what legal rights or responsibilities the registrar has, though. Obviously someone is going through them because it works and it's probably easiest for them to just ignore a request if it's not their responsibility.
Why should content be a concern, or relevant, for a registrar?
If this was a CDN then I guess that this sort of meddling could be debatable, but DNS?
So why would a glorified traffic signal be allowed to deny you service just because it disagrees with you?
I do use namecheap and don't check my email every month, so that is quite worrying.