You were right, poopipe, UVs are flipped. At first it just seemed strange to me that they could be flipped while only normal maps were working incorrectly. And even if they were flipped, I wouldn’t even think that it may be a problem for Maya. But after you wrote that you weren't sure how Maya works with flipped UVs, I…
What do you mean? When I change a parameter in material, it works like it should, as you can see in this image. But Maya inverts the textures that shouldn’t be inverted. "And when I change tangent space handedness nothing happens" - it's not a material parameter, or I'm wrong? It's like a "Shape". And when I change…