There are sooooo many different factors that contribute to how you experience a cigar on any given day, and it's good that you recognize that. What you've eaten and drank recently can have an immediate and sometimes long-lasting impact, especially for spicy foods and sour drinks. And by spice, I don't just mean pepper or hot sauce, I mean the wide range of spices to even include garlic and the like. Essentially any food or drink that you find lingers on the tongue long after you've consumed it is bound to have a significant impact on how you experience a cigar.
Also sometimes not recognized is the impact that mood and state of mind can have on how you enjoy a cigar. I've found that if my mood is off a bit, or I've been under more stress than usual, even one of my favorite sticks just doesn't quite give the same experience as it otherwise would.
As far as cleansing the palate, I tend to just go with ample time, and water to drink. If I want to get the purest experience, I won't have anything to eat or drink besides water for a good while before burning a stick, but that's rare.