Usually orthogonal means uncorrelated random variables (not necessarily independent). A good example is sine and cosine - they are uncorrelated in the interval 0 to pi. But clearly they are not independent.
Sine and cosine can be negative. Density functions cannot, and thus, orthogonality of the density functions implies that they don't have the same support with probability 1, or, said otherwise, the measure of the intersection of their support is 0.
