If someone I know and trust, someone close to me, says something, then yes I will take them at their word.

But media, and the law should not. The accused should always be presumed innocent until proven guilty. And the media has nearly as much power to ruin an individuals life as the law when they accuse someone. That power should not be exercised without good evidence.

Suppose a woman accuses a black man of sexual assault? Is it sexist to not assume he's guilty, or racist to assume he is?

We should give every accused person an opportunity to be presented with evidence and present evidence for their innocence before assuming anything regardless of the color or gender of the accused or the accuser.