They're not stopped by special walls in general. Grand total of OU viable counters to Latios (common sets): 2, and thats a fact, wanna know what they are? Tyranitar and Jirachi.
Grand total of OU viable counters to monotype Latios (similar sets): 6+, add: Specially defensive Jellicent, Amoonguss, Blissey, Chansey as well as multiple pokemon that can easily tank non specs sets that couldn't before, namely Gastrodon, Tentacruel in rain, Politoed. This is granted that you don't start running Grass Knot/Thunderbolt etc. Please tell me how these specially based walls can wall STAB psyshock :).
My knowledge of abilities is fine, I just wanted to prove to you that psychic (both as a second type defensively and as a STAB) isn't quite as redundant as you would believe.
OT: Non-weather is most definitely viable, its the fact that on non-weather teams you're restricted for choice as you will most definitely need at least 2 water resists and a way to manage Venusaur. It will be interesting to see if the tornados-t ban opens up some newer, more interesting strategies.