Do meat eaters have weaker immunity than vegetarians against colds, flus, etc.?

Not necessarily: Meat can be an excellent source of nutrition. I am wary of commercial meat from animals fed gmo foods & given hormones/antibiotics as these can be toxic, but grass-fed organic meat is very healthful and a good source of zinc, protein, essential fatty acids & other immune-enhancing nutrients. Even if one eats meat it is wise to eat a variety of fruits and vegetables.