There are 3 major reasons why blood type affects human diet.
1. Blood type specific lectins. A lectin is a carbohydrate binding protein (http://en.wikipedia.org/wiki/Lectin). The most extreme example is ricin from the castor bean. Because a single lectin has multiple receptors it can bind to many cells that have the carbohydrate on its surface, effectively causing the cells to clump together. There are three types of human blood antigen, A, B, and H. The red blood cells start off with the H antigen. The gene at the ABO locus produces an enzyme to convert the H antigen, i.e. people with type A produce the enzyme to change the H antigen to the A antigen and similarly for type B. The gene for type O people is defective so they are left with the H antigen. Some lectins are specific for for these blood antigens and will agglutinate (clump together) red blood cells for that blood type. This was first discovered by Boyd, who discovered lima beans have a lectin specific for type A blood (http://www.drpeterjdadamo.com/wiki/wiki.pl/Boyd%27s_Report_of_Lectin_Specificity). More general information on lectins at http://www.drpeterjdadamo.com/wiki/wiki.pl/Lectins.
2. Secretor status - about 80% of people have the secretor gene, which means the blood type antigens are directly secreted into bodily fluids, such as saliva and gastric mucosa. Secretor status also affects the presence of ABH antigens in the digestive tract. Consequently ABO type and secretor affect the composition of the bacteria there because some of them feed on these antigens. A general discussion can be found at http://www.drpeterjdadamo.com/wiki/wiki.pl/ABO_and_Secretor_Blood_group_Genetics. A more detailed discussion can be found at http://www.dadamo.com/txt/index.pl?3002. A related publication is at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3485159/. The authors appear to have been unaware of d'Adamo's work.
3. Gene linkage - genes are not inherited randomly; if a particular gene in the egg/sperm came from one parent then the neighboring genes on the DNA are much more likely to come from the same parent. Thus the inheritance of genes can be correlated with blood type. For humans some of these associated genes are related to the digestive system. An important example of blood type dependence is Intestinal Alkaline Phosphatase (IAP), the enzyme responsible for the breakdown of dietary fat. Type A people typically have low levels, which goes a long way to expalin why so many do poorly on a high fat low carbohydrate dies such as Atkins. There is a wealth of information on d'Adamo's websites. He does cite published research. A thorough discussion can be found at http://www.dadamo.com/txt/index.pl?1042. Other links are http://www.drpeterjdadamo.com/wiki/wiki.pl/Intestinal_Alkaline_Phosphatase_%28IAP%29, http://www.dadamo.com/B2blogs/blogs/index.php/2010/03/10/intestinal-alkaline-phosphatase-where-bl, and http://www.dadamo.com/science_bloodgroups_intestines.htm.