The acceptability of accents is heavily influenced by pop culture, which is perhaps why a high-pitched British accent may seem OK, because of the compensatory cultural value of the Britishness.
A Russian accent will not be treated as generously in the English-speaking world, after years of bad-guy one-liners being the reference point. Same goes if you have a Middle Eastern accent, or an Indian accent.
I'm sure there are many people for whom those are The Worst, but in my direct experience the worst reactions tend to be associated with accents within the US. Try speaking with a Texas accent in Brooklyn, or vice versa. Yikes.
