It depends on the job and your accent. I'm Australian and studying engineering in a university in Australia, and half of my professors have ridiculously strong accents as well as poor grammar. The university clearly prefers their research skills to their language skills, even though one would think communication is also important when they are teaching.
If you're working in customer service or something similar you will probably need to develop a more Australian accent in order to be understood well, though again it depends where you work and where you're from. There are many Chinese restaurants that employ people who are fluent in Chinese regardless of their English or lack thereof, and many Italian restaurants or gelato places that seem to seek out Italians for their Italian skills and accents.
Racist as it may be, it also depends where your accent is from. There are a lot of scam calls that come from India at the moment so any Indian-sounding accent can annoy people, whereas Western European accents are often romanticised. American or British accents are usually fine, though we *will* mock them. We will also mock kiwi (new zealand) accents, and fully expect to be mocked back. A very thick Scottish or Irish accent would be a disadvantage, as most people find them hard to understand.