This is difficult to fix completely. The preview inherits the style from its parent elements, which is why this is occurring here. This is normal behavior of HTML and CSS.
I have made some CSS changes for the next build that should reverse any styling that the default BB-Codes might add. As for custom BB-Codes, that should probably be handled on a custom-basis, but I'm not sure the div would inherit much else than what's already been accounted for.