Must admit, while I have to be pedantic about the meanings and spellings of words for my job (sub-editing/proofreading), it never occurs to me to be similarly pedantic about how people speak.

I can't see that one can possibly cordon off "sloppiness" from accent: "sloppiness" is what dialects and accents are predicated upon. "Sloppiness" in this context is simply an ideologically charged synonym for "variance".

Like most discussions concerning rectitude or etiquette (of anything at all), this one revolves around class. When I do my weekly volunteer reading session with local primary school kids, I'm well aware that the Afro-Caribbean (in the main) pronunciation of "asked" as "axed" that a lot of the kids use would count against them in a job interview in the industry that I work in.

You've got to know, for strategic reasons, what other people consider to be right and wrong. But you've also got to know that those people are pedants whose pedantry is a mask for protecting their own kind against meritocratic incursions (such as improving A-level results from state schools).