Does 'non-standard dialects' sound normal(natural)? Aren't all dialects non-standard?
A dialect is a particular form of a language. Some become adopted as national or regional standards. The dialect of English spoken in the "home counties" between London, Oxford and Cambridge became the standard dialect of British English.
So dialects can be standard dialects, like British English. Or non-standard, like Cockney. What is standard in one place may not be standard elsewhere. Standard American English dialect is non-standard in the UK.