All important decisions must be made on the basis of insufficent data.
-- Sheldon Kopp in An Eschatological Laundry List
No offense, but I suspect many people will consider your question a little lame or simplistic. However, it's really quite intriguing - almost a paradox, in fact.
We could take a couple steps back and first ask whether democracy is the best form of government. That, too, is an intriguing question, considering the fact that there have been dictatorships that made the U.S. democracy look like a joke.
But if you're going to choose democracy, then it doesn't make much sense to not get the most out of it. Democracy requires citizen participation. It could thus be argued that people living in a democratic state have a responsibility to participate in government. And since ignorant people make lousy voters, we could further argue that citizens have a responsibility to educate themselves.
But not everyone has an equal education. In the U.S., there are a frightening, almost unbelievable, number of people who are frankly stupid. We might therefore change your yes-or-no question into something else:
Should everyone participate in a democracy?
One of the key words is "participate." Are we talking about voting, protesting, vigilantism or what?
To be perfectly honest, there are many - probably millions - of people here in the U.S. that I personally wish weren't allowed to vote. But someone has to participate, or you don't have a democracy at all. And if you want a healthy democracy (and society), that participation has to go beyond voting.
In general, I think participating in a democracy is not only ethical but a responsibility. However, I think it is unethical for certain people to participate - the people who knowingly vote for a corrupt candidate or who only think about their own special interests when voting.
However, the answer may vary somewhat between democracies. If your democracy is extremely corrupt, so much so that the election system is a total farce, then the rules may change. If there are no good candidates to vote for, then your participation has obviously been limited. However, there are other ways to participate, including political reform or even revolution. Or you could simply move to a country with a functioning democracy - or a dictatorship that actually works for the people.
In summary, politics is a part of life, and if no one participates - whether your government is a democracy or a dictatorship - the only people who benefit will be the ones in power...and you know what they say about absolute power.