Sorry my statement was very poorly phrased. What I meant was, self sacrifice is not a duty imposed (or even encouraged) on you implicitly or explicitly in a democracy (like voting is, for example). It's only a duty if you believe it is. Yes, this is a tautology, but you seem to be asking for a specific answer to a question that inherently depends on each person and each situation. The majority-minority dynamic further complicates it (i.e., if you are in a minority of Americans who cares about what the NSA is doing, do you have a right to sabotage or expose what they are doing, despite being against the majority?).
As for harmful to a minority, you're thinking of winner-take-all electoral processes. Democracy is usually meant to describe the overarching idea of self-rule with checks and balances. I can't think of a single democracy in the developed world that doesn't have a minority-friendly self correcting feature (whether or not the checks and balances are working properly is a different matter).
To me it comes down to, do you "believe" in democracy or do you actually BELIEVE in democracy? The former means that you don't actually give a shit about the type of government you are ruled by until it infringes on you and yours. The latter means that to you, living in a democracy and being free (from oppression, surveillance, an over-zealous majority, etc.; whatever freedom is for you) is as important an aspect of your identity as your job or your family.