The cut and dry definition of preachy is a term said to describe a person who is more times than not, giving advice in an irritating way: giving, or in the habit of giving, advice on morality or behavior, especially in an irritatingly tedious or overbearing way. This term is mostly associated with overtly religious people or people with controversial opinions or ideologies that try to shove their opinions down your thought. Some examples of people who might tend to be preachy are those bible thumpers who try to tell you what to believe, atheists who want to try to tell religious people that their ideas are invalid, the hippies who tell you to hump a tree, or the radicals who try to make people believe irrational conspiracies that make them feel good. Most of the time, preachy people only piss off those they try to sell their ideas to, and end up having a lot of haters, and a few dick riders.
Dude#1: "I had to hitch a ride with our neighbors last night and all they did was talk about how all gays should die."
Dude#2: "They're just preachy motherfuckers. Ignore them."