It is possible to care about multiple issues simultaneously. Saying it's demented to care about one person being wronged because other, totally different people are wronged is a bit selfish. It's okay to have a purpose that you believe in, but the world isn't black and white.
> "spending time worrying about false rape accusations in the present environment is demented."
I'm sorry, but not being concerned that some statistically significant portion of rape accusations against fullly innocent individuals often utterly destroys their lives just as much as being raped often destroys that person's life is demented. Both are absolute vile tragedies and should not occur in a truly civilized society. There's something deeply wrong and broken with the people who commit either of those acts.