Well, not necessary silly, but it is not the only dimension on which people and nations might align themselves. Being left-wing or right-wing are not enough to define any person or movement thoroughly. The supposition that a right-wing government could never support a left-wing movement in another country is refusing to understand any orthogonal things exist.

For instance, I consider myself right-wing by local standards, but when looking at how things go in Turkey, if I must choose a party to support, I would pick the one that's a member of Socialist International. Still, I think that does not make right-left split totally silly.