I mean that depends highly on how you protest and what that protest is meant to accomplish.
Like what you seem to have in mind is that a minority of protestors forces the government to do something in their favor, thereby getting around the necessity for a majority or even consensus affirmation of consent.
And the thing is whether that is unethical or not kinda depends on what they are asking for. Like do they want privileges or is the system as-is so unbearable that it needs to change as soon as possible? Well in the former case you could argue about it being unethical and the latter you might even argue that the system is unethical while the action is just necessary.
However what that would be is "undemocratic". Because you shifted the sovereign of the country, which in a democracy should be the people, to whatever group is actually making the rules of the game, either explicitly (the government) or implicitly (whatever lobbying group has the most influence on them).
And contrary to popular believe voting =/= democracy. Voting is usually a democratic act because the legitimization for any ruling comes from the people, who are thus the ones who make or break a government. And that is usually done without making preferences among them so that no individual has more power, which would defeat the ideal of democracy, because that person would rule rather than the people.
But if it were just a vote then democracy would end right after the election. Because after that the person/group in charge would no longer be the people but the government. So ideally any power that a government holds is just the ability to speak with the multitude of voices that gave them their trust. Or ideally not even their trust but their mandate to do a certain thing that they promised to do. Which is often conveniently forgotten after the election.
And conversely who could hold them accountable and revoke that trust and mandate. Otherwise the power would come from the institution not the people. Usually you might have rules and regulations in your constitutions or whatnot to impeach a government, demand reelections, sue them or whatnot.
Also often there are 2 ways to interpret representative democracy, one way is that the people are able to chose their representatives, the other is that the representatives are the ones to actually practice democracy. Like they have these regular plenum meetings, the discussions, negotiations and votes on what should be done on the issues, that you would expect from a real, direct, no adjective democracy.
So whether that counts as a "real" democracy is something that you can hotly debate. It has some features that are undemocratic like institutionalized power and free mandates (voting a person, not their policies and not being able to return them before time) on the other hand compared with other systems it's usually still more democratic than many other systems, so one often agrees on grouping in somewhere in the spectrum of democracy.
Anyway back to protesting. So first of all this forcing the government to do something overriding consent is hardly the only thing that can be accomplished by protest and many protestors don't even dream of getting there that easy. Like first of all it's just raising awareness of certain points. And if that creates a discussion about the issue, then that is perfectly valid within the scope of democracy.
Though it opens a whole different can of worms in terms of who has a right to attention. Is advertisement unethical, is placating every free space with ads unethical, are demonstrations and protests unethical, are public speeches unethical, is broadcasting unethical. Generally speaking there's nothing wrong with it and being able to hear different voices and being able to gather your information freely is a prerequisite to making an informed decision which is the basis for having a truly democratic process. Otherwise the one controlling the information shapes the narrative and is ruling, not the people.
And so usually democracies try to make that as free and accessible as possible to everybody, but there are still elements that are tricky. So who is allowed to get "in your face" with their narrative and who isn't. Who's got the time and resources for that? Are those equally distributed? If you have them all just write up their stuff and drop it somewhere, who's providing the search&sort function algorithms that almost inevitably favor one thing over another? Like people naming their kid AAron cause of the alphabetic advantage and shit like that.
So yes there are a ton of pitfalls as to what can be used to subvert the ideal of a democracy. Though at the same time you kinda need mechanism to petition and raise awareness for problems, because given that the state of democracy is hardly perfect, that is also vital to become aware of these pitfalls and patch them.