The late Dr. Benjamin Spock, arguably the most influential pediatrician of all time, has left children and their parents with a surprising and rather demanding legacy: advice that they stick to a vegetarian diet devoid of all dairy products after the age of 2.

In the seventh edition of his world-famous book, ''Baby and Child Care,'' issued last month by Pocket Books just weeks after his death at age 94, Dr. Spock recommends an approach to childhood nutrition that many experts, including his co-author, Dr. Steven J. Parker, consider too extreme and likely to result in nutritional deficiencies unless it is very carefully planned and executed.

''We now know that there are harmful effects of a meaty diet,'' the book says. ''Children can get plenty of protein and iron from vegetables, beans and other plant foods that avoid the fat and cholesterol that are in animal products.'' As for dairy foods, Dr. Spock says, ''I no longer recommend dairy products after the age of 2 years. Other calcium sources offer many advantages that dairy products do not have.''

Given the influence of the book, pediatricians and nutritionists have reacted with concern to the recommendations to raise children on an all-plant, or vegan, diet. Throughout its 52-year history, ''Baby and Child Care'' has been the second-best-selling book, next to the Bible.