There are three questions in the title. I will answer them in reverse order!
Why do white cats have white fur?
Cats which are completely white have a gene in their genetic makeup which is called the dominant white gene. It stops the development of cells in the skin that produce pigment. These cells are called melanocytes. They fail to migrate to the skin during embryological development. Melanocytes produce pigment and as there is a lack of them in the skin pigment is not produced. Pigment is melanin. In white cats, the hair strands don’t contain melanin. Therefore, they appear to be white. It is actually transparent as there is no pigmentation inside the hair strands. I guess it just looks white when it’s all bundled together.
RELATED: White cat coats.
Why do white cats get sunburned?
Not all white cats get sunburned but if a domestic cat is going to get sunburned it will likely be a white cat and it will likely be their ear flaps. That’s because there is little fur on the ear flaps and what little fur there is has no pigmentation in the hair strands. Therefore, the ultraviolet light goes straight through the fur onto the skin and burns it. There is no protection from the pigmentation. The same reason is why people of colour are much less likely to be sunburned than pale-skinned, red-haired white people.
Ultraviolet light causes skin cancer because too much UV radiation from the sun can damage the DNA in a cat’s skin cells. The DNA tells the cells how to function. If the DNA is damaged to a sufficient level, it causes the cells in the skin to start growing out of control which can lead to skin cancer. Skin cancer of the ear flaps often results in their surgical removal as seen above.
Why do white cats get eye boogers?
White cats don’t get eye boogers any more than non-white cats in my opinion. The phrase “eye boogers” refers to a buildup of a kind of mucus that comes off the cornea of the eye and congregates in the corner near where there is a tear duct and above (see diagram). If the tear duct is blocked the liquid runs from the corner of the eye and down the side of the nose. If the cat is white then this is very apparent because it stains the cat’s face.
I think the reason why people perceive white cats as having more eye boogers than non-white cat is because we see a lot of white Persian cats on the Internet because they are popular. The contemporary Persian cat is very flat-faced. This distorts the anatomy of the face. The tear ducts which drain tearing from the cornea of the eye become blocked because they are distorted. This causes tears to run down the face instead of through the duct. This stains the face. You will see a lot of white Persian cats with stained faces caused by tear duct overflow.
In non-Persian cats you might see tear duct overflow sometimes but relatively rarely because they are white and tear ducts contain dirt which is coloured and therefore, they stain the white fur. You can buy special treatments for tear duct overflow such as Johnson’s Diamond Eyes (see above).
Below are some articles on white cats.