There are two views about what constitutes a vegetarian diet. One view which is rather extreme excludes not only eggs but also milk because they are regarded as animal product. A further extreme form excludes even tubers and roots since they are regarded as living as they continue to grow giving rise to many more. Obviously, this view takes its stand upon non-injury to any living form. It is more like a moral principle that is often arbitrary and based on a limited understanding of life itself. From the spiritual perspective life is everywhere even in the atoms and stone.
If we take the consciousness perspective which is more complete and based on fundamental truth of creation, then taking eggs and of course milk is perfectly fine, especially since unfertilized eggs are invariably vegetarian.
About Savitri | B1C3-04 The Growth of Divinity in Man (pp.25-26)