Interesting one, this. While hate might be a bit strong, the teams I hate Wire losing to are, naturally, Wigan, Widnes and Saints, in that order (admittedly this hierarchy dates from the 80s when I watched Warrington properly).
The trouble is that teams become increasingly 'hated' in proportion to their success. I wonder how many fans of other sides actively 'hate' Warrington - not many, I'd guess, as we haven't been good enough to induce enough enmity in recent years.
My dad had a different take on the local rivalry stuff, though - he'd support any Lancashire team over any Yorkshire side. So, any televised game years back, I'd be going for Cas or Hull or Halifax or whoever, and he'd happily prefer to want Widnes, Saints or Wigan to win

Mind, he got a bit bored of this stance when Wigan won everything.
Favourite other teams: Hull KR, Castleford and London.