Polarizers can have different strengths. Technically they should all be similar, since theoretcially they should eliminate all waves perpendicular to the axis. But that's theoretical, and cheap polarizers might not be efficient. What brand?
It's unlikely it's a complete fake, but I wouldn't be totally surprised if you bought a cheapo somewhere. I've seen plenty of polarized sunglasses that aren't.
One thing: technically it's not 90 degrees to the sun, it's 90 degrees to a reflected surface. The reflection has become polarized, which allows the polarizer to block it. The effect on blue sky can vary, depending on how much reflection (haze) there is in the sky. The best way to check that it's working is to look at sunlight reflecting off of something, like a shiny object.