I think there is subtle racism in the form of romanticizing it when European people speak English with their heavy accent and despising it when an Indian person speaks English with their accent. That's the truth and you always have to work around it.
You can of course put some conscious effort in to having less of an accent.
I've sometimes had difficulty making myself understood with my Dutch accent, which isn't always very practical. Especially in noisier environments and over the phone it can be annoying.
On the other hand, I also see it as just who I am. Would you ask an Irish person to change their accent? Of course not; it's part of their identity. On the other hand, if someone with a strong Irish accent would move to the US, NZ, or even the UK it might be wise to tone things down a bit so folk actually understand what you're saying. And asking where the craic is at would likely be received similarly to Checkov asking where the nuclear wessels are.