Letting My Characters Be Themselves

Sometimes my characters say things I disagree with and do things I never would.  Rarely, I censor them, for example if it wouldn't be that big of a deal, wouldn't hurt the story or take away from their character.  But usually I let them be who they are  This comes with some risk.

If a protagonist says something I disagree with, I worry that my readers may think I would also say something like that.  Oddly, I'm more worried about offending people I do know as opposed to complete strangers.

Somet...