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Do you mean American mumbling accent or International English accent?> Indian English has as many rights to life as have German English or Texan English or Aussie
You are missing the point. It's not about "rights to life". No language (or dialect, or idiolect, or accent) has a "right to exist", or they all do. Who cares? (Also, German English? wtf?)
What matters are things like: Are you getting the results you want? Are you delivering good value to others (so that they want to give you good value back!)?
If your job doesn't require communication, speak whatever you like. If you're so damn good at your job that everyone else has to obey your whims, AND you don't care about the total effectiveness of your team, then speak whatever you like. But most people need to communicate, and for some people, poor accent becomes a dominant factor in their job performance. The responsibility is shared, but it falls most-heavily on the person who is most-different, because it's easier for one person to change than for a whole office to change. This, I hope and trust, is what znt meant when he said "professional responsibility".
Sometimes it cuts the other way, though. I'll give you an example from my own life. I am personally bad at understanding thick south-asian accents. I used to think all people from my background (Canadian anglophone) had the same problem. But I'm learning that I have more trouble than most people. That means it's mostly my problem. But if everyone agrees that so-and-so is very hard to understand, then it would be mostly so-and-so's problem.
This isn't about "rights" or "entitlement". It's about being effective. It's not the "law of the jungle", it's the law of gravity. And it's laughable, stupid, and somewhat offensive, to say that we might as well go back to slavery.
(Of course, sometimes I hear someone say "you have no right to speak your own language in my country". Those people are stupid and wrong. Fortunately, most people who say things like that are also not very good at other things in life, and they usually get punished by the marketplace, and we can ignore them. The rare people who are both powerful, and also stupid xenophobes, everyone else should cooperate to punish such people.)