Can white eggs be considered as non-vegetarian?
Of course eggs are not vegetarian. Eggs are, well, the eggs of chickens (usually). Chickens are animals so their eggs are animal matter as well. Whether or not the egg has been fertilized is completely irrelevant, eggs are chicken just as much as drumsticks are.

The color of the egg has nothing at all to do with it. All eggs are, by definition, animal cells. Basically, the chicken's egg is the equivalent to the human ovum. In both humans and chickens, the female will regularly produce eggs and discard them. In the case of a human woman this is the monthly period. When an egg is not fertilized, it is discarded along with some cells of the wall of the uterus. Similarly, in chickens, the female produces and lays eggs. If an egg has been fertilized, it can grow into a new chicken. If it has not been fertilized, it cannot become a new chicken but is most certainly still an animal cell.   

So yes, eggs are most certainly animal, not plant or any other kind of matter. Whether or not you should eat them is up to your own moral guidelines to decide. While they are animal tissue, no animal has been killed to obtain them and no harm comes to the chicken if we harvest them.