Put Up, Not Shut Up
We live in a world where most people in 1st World countries have freedom of speech, the right to say what's on your mind as long as you're not one of those idiots who yells "fire" in a crowded theatre. We also live in a world where people think that freedom of speech also means freedom from judgment for the things you say, and that receiving criticism is tantamount to being told to stop talking entirely. There is a difference between "being silenced" and "being held accountable."
It's amazing how many people haven't figured that out. When someone says something they believe to be true, or that is their opinion, and someone else says something that contradicts it, it is surprisingly common for the first person to jump straight to the defensive as if their very liberty is being challenged. "This is America and my freedom of speech gives me the right to say whatever I want!" First of all, no, it doesn't. Saying things to start a panic is still illegal, and will land you in jail. So stop that train of thought right there.
Secondly, your freedom of speech ends with the government. Freedom of speech means the government will not attempt to stop you from saying whatever you want. It doesn't mean the people you're talking to have any obligation to listen, or to not kick you in the throat if you insult them. If you call the owners of a website a bunch of assholes, they might ban you for it, because it's their website and they can do what they want on it. Where's your freedom of speech now? Further, it doesn't mean you get to say what you want without being questioned about it: if you say something that looks like bullshit, people are going to call you out on it. Freedom of speech is not freedom from consequence.
If you say something like "most republicans are racist," there is no way for you to know that as fact - there are an awful lot of republicans, and you're never going to get an exhaustive survey out there to prove your point. What you're doing in such a case is called spouting bullshit. You're making a magnanimous claim about a group of people without interacting with or surveying more than a handful of them, and who knows how or whether you actually did that in the first place? You are not in a position to claim anything about "most" republicans.
This is a claim you should expect to get called out on. And when someone does that, they are not silencing you; they are calling out your bullshit. If you mean that most republicans you've talked to at conventions are racist, it is your intellectual and ethical responsibility, instead of saying "most republicans are racist," to say "most republicans I talked to at conventions are racist." This is something that pollsters do constantly: they always say "64% of those polled said [whatever]," because context is critically important.
How you talk to people to get your information is important too. You know that one study (and there was precisely one, out of hundreds undertaken) that asshats like Jenny McCarthy like to cite, that says there's a link between vaccinations and autism? It was published in a British medical journal called the Lancet. Then it was discovered that his method of research was to hand pick 12 children with autism, from families who supported the outcome he wanted to prove, and to edit their medical histories as required to support his claim. It was also revealed that he was on the payroll of a company that was developing a competing product to the vaccine, which is only a massive conflict of interest. When the context was discovered, the Lancet retracted his paper from publication, issued a written apology, and the doctor was stripped of his medical license. Freedom of speech allowed him to say there was a link between the two - but accountability said he was full of shit, and he was treated as such.
Freedom of speech also doesn't mean you get to make up your own facts. I recently watched a YouTube video from 2008, in which it was posited that Barack Obama is Osama bin Laden. The "evidence" presented was to overlay pictures of the two so that the facial features more or less lined up, and then claim they're the same. When I pointed out that they're obviously not the same person, and anyone who thinks they are is an idiot, I was shouted down because "if some people want to believe this is true, that's their opinion." No, it's not. An opinion is "Rush is the greatest rock and roll band in history." An opinion is "this kiwi fruit tastes bad." Believing something that's plainly false to be true is not an opinion, it's a delusion, and people do not have to respect it or the person saying it. If you say to me that Obama and bin Laden are the same person, then after I laugh in your face I'm going to tell you to prove it. If your evidence is not compelling, I'm going to laugh in your face again and call you a fucking idiot. And then I'm going to laugh in your face again. And you'll deserve it.
When someone calls you out for saying something you're in no intellectual position to say, they are not attempting to silence you. They are holding you accountable for your words. If you say something, especially if it's a claim you're stating as fact, you need to be able to back it up. If you're stating an opinion, make it clear that it's an opinion, and be ready to explain why you came to it. If you're claiming something as fact, be ready to provide documentation to back up what you're saying. Otherwise, don't be surprised if someone calls you on it, and don't go thinking they're trying to silence you for daring to say something against what they believe. They're challenging you on an intellectual level to prove that there's standing for what you're saying. If you don't have any, then you need to stop throwing bullshit around.