While it is true that both rules cancel each other out for the purpose of striking order and the asf rerolls of your oponents, they do not, however, cancel each other out for the purpose of rules like «Blizzard aura» and Bironna's Timewarp which grant always strike last and always strike first.
A model can only ever have these special rules once, even if they are both present and cancelled in the same model, it cannot gain another, non-cancelled additional instance of either.
For any reason.
I have no clue why it works like that, but that's how it's ruled all over the place, according to my gaming club and to Ulthuan.net.
I fled to chase dreams that I can't yet describe.
I wake up, shivers, I hope my dream wasn't you.
But son, your dad, it ain't me, it can't be.