There are several reasons you might want to avoid dairy products: lactose intolerance, a commitment to veganism, or simply a dislike of cheese and milk. But "because they complicate digestion," as I read in one magazine, is not one of them.
If you're lactose intolerant, the sugar in milk will sail through the gastrointestinal tract without being processed, says Amy Foxx-Orenstein, past president of the American College of Gastroenterology and an associate professor of medicine at the Mayo Clinic. That can lead to bloating, gas, and other unpleasantness. Folks experiencing flare-ups of celiac disease or irritable bowel syndrome might also find milk hard on the stomach, she says. And, says Suzanne Havala Hobbs, a registered dietitian and faculty member at Gillings School of Public Health at the University of North Carolina, people with acid reflux may experience symptoms if they eat a lot of high-fat cheese and then loll on the sofa. But otherwise healthy people without those problems aren't going to be harmed by dairy—and cutting it out certainly won't provide any magic weight-loss advantage.
Moreover, the whole notion of "complicating" digestion is puzzling; actually, the harder your system has to work to break down food the greater the boost to your metabolism, says Foxx-Orenstein. And more complex foods like whole grains can keep you full longer than more processed and easily digested ones.