That's not true. CSP can have a specific host/path for scripts and won't even run JS in the page without explicitly opting in to 'unsafe-inline'. It's an important prevention technique against XSS for pages showing user generated content.
My point is that if GoDaddy modifies the HTTP body, they could as well modify the CSP you send in the HTTP header. It is yet another stop-gap, but the real solution is to get a hoster you can trust.