We do need a final solution to the current problems, which is basically a war of a kind.
Like the war on terror, you mean? What will this one be called? "The war on terror and then some", perhaps?
Apart from Katie, no one knows in which context she used the the expression final solution.
But no one is able to describe any plausible alternative context, either.
Can anyone honestly claim that she is suggesting that Muslims should be gassed, put in ovens, worked to death or sent to concentration camps?
Yes. That is what it means.
Before we look for a final solution, I'm not aware that we have found a first solution yet.
If there was a "first solution" it sounds like it hasn't worked. So it wasn't a solution.