Is there a moral reason to do what Hitler did not and to avoid what he
did because it was he who did or did not, respectively?
It sounds like you're asking, is it OK to endorse vegetarianism, citing Adolf Hitler as an example of vegetarianism?
It depends on the context/situation, but you probably won't get much mileage out of such statements because Hitler has been so demonized.
I would actually like to see more comments about Hitler's good side to balance the insane demonization that makes it almost impossible to know the truth. I would also like to see an end to the use of Hitler and the Nazis as a metaphor for evil incarnate.
What about the Romans, Spanish and British, who carved empires out of blood? What about Caligula, Vlad the Impaler or U.S. President Andrew Jackson?
How was Hitler worse than Stalin? And how was he more racist than Churchill, Roosevelt or the French?
Focusing more closely on your question, I wouldn't say it's unethical to invoke Hitler as a symbol of clean living. But it wouldn't make much sense, because most people would have a mini-mental breakdown. You'd be better off replacing Hitler with Obama, who murdered so many innocent people with unmanned drones.
Is there a moral reason to do what Hitler did...
Like not smoking? One could well argue that not smoking is a moral act, but linking it to Hitler or anyone else doesn't make much sense. It's a moral act all by itself. If 10,000 nuns smoked, not smoking would still be an intelligent (and quite possibly moral) choice.
To further put this question in perspective, just replace "Hitler" with the name of one of history's biggest monsters, like Caligula, Abraham Lincoln or Milton Friedman.
Many people regard Lincoln as an all-American hero and might therefore appreciate using his image to promote drinking milk or whatever good things he did. However, Lincoln also presided over the biggest mass execution in American history and may not be too highly admired by Native Americans.