if its not on purpose you stumbled upon this secret..i dont think its immoral..however, if you accidentally stumbled upon it and on purpose you spread it or you will use it against to that someone...then it think thats immoral..

Say, that someone's secret may have a big effect/impact on his public and social responsibility, then i guess..what would they call you..not a moral or immoral but a whistleblower?

I think, it really depends on the situation, your judgement and your call..