I believe Rimmer is technically correct, but whether you use "Idealistic me" or "Idealistic I" is kind of secondary, they both sound awkward.
I would suggest rewording the sentence, depending on how you intend it to be read. In my opinion a much more eloquent construction would be:
Being idealistic, I decided otherwise.
Or, you could say "my idealism" instead of "Idealistic me":
My idealism caused me to decide otherwise.
You could also use "my idealistic side" to be a little more causal, like:
I was tempted to cheat, but my idealistic side kept me in line.
As Eduardo pointed out the original construction only makes sense if this is a person describing his inner character to another:
Greedy me wanted to keep the money, but idealistic me decided otherwise.