It depends. Certainly there are professions where it absolutely matters such as the entertainment industry and newscasting. On the other end, there are professions where people are much more concerned about what you do than how you speak (especially when many people from all over the world work there) such as computer programming.
Location also matters. What can sound like a country bumpkin to a Londoner could be considered pleasantly exotic to a New Yorker and vice versa.
And who you will be talking to in the course of your duties matters. Accent can be a sign of economic status and sounding like the people you are dealing with tends to make them trust you more. So people in professions that deal with people of a higher economic status frequently are often rewarded economically for changing to the accent used by those people. Particularly if they are in sales.
And of course it is critical that your accent be understood. I remember the first time I was in the the US Deep South in the 1960s. I could barely make out what people were saying. Someone with the thick accent that many southerners had at the time (TV seems to have ameliorated it some in today's world) would have had great difficulty being understood in New York or Chicago because the accents were so far apart as to almost be different languages. If people who do not have a hearing loss keep asking you to repeat what you said, then you might need to look at changing your accent. And even those of us who do have a hearing loss find it easier to understand people who speak in a similar accent to the one we have.
And of course hiring officials are all different. What is off-putting to one person is ignored by another.
So it may matter or it may not, but will there be any harm in changing your accent so that it doesn't matter? It could improve your employability and it most likely will not harm it. It may mean, though, people from you home area will think you sound stuck up when you visit.
On the other hand if you move to a different geographic area and work there for a few years, your accent is likely to get closer and closer to the norm for the area where you live. So if you can find a job in that are and you don't have difficulty making yourself understood, then likely the problem will go away in a relatively short time with little effort on your part.