I think that you have to categorize a little more clearly for this question - many posts have brought this up, but for example, I don't consider my father in law a "cheater" even though he routinely improves his lie, does not putt out completely, takes mulligans, etc. He is playing only for his enjoyment, and as a matter of fact, doesn't even keep score anymore. However, he is a pleasure to play with, and since he is not keeping score, nor sticking completely by the rules for himself, he plays rather quickly. He is playing as what I would call a "recreational only" golfer. I do play by the letter and spirit of the rules, call all applicable penalties on myself(when I know the rules), etc. I would call myself a "competitive" golfer. By that I do not mean that I play in a bunch of tournaments or try to win money, or whatever, it just means that I keep score, and keep a HCP index, and use it to compare myself against other golfers and the course I am playing. I wouldn't call anyone who falls into my personal classification of "recreation only" golfer a cheater, because they are not technically playing the same game as I am. As long as they follow good etiquette, and can keep pace, do they really bother you? (They may, but that is a matter of personal preference.)
The ones that bother me are the "competitive" golfers who cheat to gain a perceived advantage over others. Either sandbaggers, or straight cheaters. Sandbaggers bother me more, as they can be seen on the course following all the rules, and scoring exactly what they get (or even calling "extra" penalties on themselves to boost scores) and then when it comes time for that club tournament, they routinely shoot 5-10 strokes below their handicap.
If I could use my designations, I would rather play with a high handicap competitive golfer or a recreational only golfer, as long as they know and follow decent golf etiquette, and can keep a decent pace. I don't mind slowing down for other players too much, though.