You cannot say:
Because opinions have been oppressed in the past.
This is true but the oppression of opinions was to try to force on opinion to be dominant over others through force. This doesn't make an opinion any more useful than before. The legal right to an opinion doesn't mean your opinion matters.
Because of the political process/voting.
Your opinion is barely, if at all, reflected by politicians that you elect, outside of what politician you think would be the best candidate. Also, you can vote for a politician and have them lose, making your opinion borderline worthless.
This isn't a debate about censorship or oppression, so keep that shit out of there. We're asking, in a situation where that oppression does not exist, what actually "makes" your opinion "matter", in the long run?
I argue that personal opinions are borderline worthless outside of in fields of expertise. Why? Because your actual ability to influence others is pretty much naught unless you have the skill, experience and persuasive power to actually convince others to agree with you, and because you're in the same situation as about 99% of the other 7 billion fucks that you share this planet with.
Now on a smaller level such as internet forums you can argue that you are able to convince others to change their opinion quite easily but again, these people also don't really have the ability to
You might argue that a large pool of opinions might be useful, but I disagree again. The large pool first off does not reflect the opinions of all of them inside but rather a normalized group of opinions that people will either somewhat agree with or somewhat disagree with, and this determines whether or not they are a member of that large pool. Secondly, while a large pool of people can definitely have influence on opinions on a much larger scale, we're still met with the same problem of "who cares?".
Let's consider this. Let's think about how difficult it would be to force a country to accept homosexual marriage. Not the hardest thing on the planet since it only changes the marriage certificate from having different sexes to having the same sexes, at least in terms of legal woes. But it has taken hundreds of thousands of people and decades to even reverse this extremely simple problem, and really only so that people can shut up about it.
There are literally hundreds of political influences much much more powerful than just something simple like gay marriage that we will basically have no fucking control over and we will have to tolerate it.
Now what cases do I think opinions matter much more? When you have results backing those opinions and present a case that makes the opposition look like such a retard that they can't keep perpetuating shit. In politics this is much easier said than done, but in many other things in the world that have jack shit to do with politics (like science, technology, and other scientific advancements) people have the potential to educate themselves to the point of becoming an expert and being able to formulate opinions that truly matter, and have the results to force people to respect them.
And when I say "respect", I don't mean "agree', I mean "taken seriously". Do you seriously think any high end person really gives a fuck about what any of us tarts have to say? They're only going to spend their time talking to people who actually understand what they're talking about.
And even then, don't expect to "change the world" unless you can produce results.
I feel that a lot of time is wasted on having opinions without actually gaining the results to back them up.