Not all rabbits have red eyes, only albino rabbits have red eyes, although some colors do have a "ruby glow" to the eyes.
Eye color has to do with the concentration of, or lack of, pigment in the eyes.
Fully pigmented rabbits have brown eyes, dilute pigmented rabbits have blue/grey eyes.
Shaded rabbits (such Siamese-colored) have brown or grey eyes with very little pigment so that the eyes shine red in low light.
Red-Eyed White rabbits are true albinos and have no pigment whatsoever, so what you're actually seeing is the blood flowing through the eyes.
The Californian (white with black nose, ears, feet, and tail) also has red eyes, he's a partial albino that's sensitive to temperature, during hot weather his dark points fade out.
Then there's another gene mutation that creates a White rabbit with blue eyes, called the Blue-eyed White -- these rabbits are not albinos, as there is pigment in the eyes.
Rabbit breeder 12+ years