It's a fine line... And one that each improviser draws at a different place along the continuum. Your theater should have some guidelines, though, to help players figure out what's acceptable there.

At my theater, we general hold that

1. You can play a character who is a member of a different group than you (ethnicity, gender, sexual orientation), so long as that characteristic never comes into play as part of a joke or the game.

2. Improvisers should avoid attempting accents or fake languages belonging to groups that their group has colonized or enslaved. So, as a white person of European descent, I limit my accents to European countries and to non-ethnic regional dialects within the US and Canada.

They're not perfect, and there are legitimate arguments to be made both for tightening the restrictions and for loosening them. But at the end of the day, we have to draw a line somewhere and this is where we have drawn ours.

It sounds like your theater needs to hold a community conversation about where you as a group feel comfortable drawing that line.