Suppose a certain senator -- call him Senator Fred -- makes a controversial statement. Another member of Senator Fred's party is likely to be asked whether he agrees with that statement.
The evasion goes something like this:
Question: "A member of your party, Senator Fred, has made a controversial statement. Do you agree with what he said, or are you going to denounce what he said?"Notice, the question hasn't been answered. The matter of whether Senator Fred has a right to make a certain controversial statement -- or, more broadly, to hold controversial beliefs -- is not at issue. The question was whether Senator Fred's colleague is going to agree with the senator's comment or disagree with it.
Answer: "Well, Senator Fred has a right to his opinion, he has a right to believe it and a right to say it."
Politicians and pundits usually want to avoid both of those choices, though. On the one hand, agreeing with a controversial statement or belief could land them in trouble with voters. On the other hand, though, denouncing a fellow party member can land them in trouble with their party.
So, they try to manufacture a third way, a way out of from between a rock and a hard place, by changing focus to the right to freedom of belief, or freedom of speech. Few people, of course, are going to disagree with these rights, so the person who uses the "they have a right to their opinion" evasion can say something that most people agree with while appearing to have answered the question they were asked.
But, really, they haven't answered the question. They've just managed to skillfully avoid answering it. And they usually get away with it.
So, what should we do when we see someone employ this evasion?
The thing to do is to point out that they're answering a question that wasn't asked, and failing to answer a question that was asked.
For instance, you should say something like this:
"I'm not asking that, we all agree he has that right. The question is, do you agree with him? You have a right to agree with him, a right to denounce him, and a right to be silent on the matter: which right are you going to exercise?"Or, say:
"That wasn't the question. I didn't ask 'Does Senator Fred have a right to believe or to say X?' Forget about Senator Fred altogether. Focus on the statement itself. Do you believe that statement is true?"Responses along these lines will hopefully put the answerer on the spot, and make them give up on this evasion.
EXAMPLES AND ANALYSIS
QUESTIONER [unidentified]: Talking about the comments that came up last night, the statements by this questioner talking about President Obama being a Muslim, talking about Muslims being a problem in this country. You just said that question is offensive to the press, is it not also perhaps offensive to the millions of Muslims in America?-- Republican presidential candidate former Sen. Rick Santorum (R-PA), September 18, 2015, responding to a question concerning remarks made at a campaign event for Republican presidential candidate Donald Trump. At Trump's event, an attendee said Muslims were the problem with the country, and Trump did not challenge the remarks.
SANTORUM: Here's what I have to say about that. People are entitled to their opinions. We have a First Amendment for a reason. People can just stand up and say what they want. You don't have to agree with it, you don't have to like it. I have a lot of events where people get up and say things that I don't like. I have a lot people say things about me that I don't like. Read my Twitter feed. But I'm going to defend your right to say it. Whether I disagree with it or agree with it really isn't the point. The point is, do they have the right to say it, and do we have an obligation to correct it? And my answer is yes, they have a right to say it, and no, we don't have an obligation at a town hall meeting to correct everything that someone says that we disagree with. … I'm not playing this game that you guys want to play. The President can defend himself, he doesn't need Rick Santorum to defend him. He's got you doing that very, very well. So cut it out. … It’s not my job, it’s not Donald Trump’s job, it’s not anybody’s job to police a question. The questioner can say whatever he wants, it’s a free country.
Comment: Santorum is knocking over a straw man: no one has suggested that the remarks made at the Trump event should be illegal. Freedom of speech – as enshrined in the First Amendment – allows people to make remarks like the attendee at Trump's event, but it also allows people to criticize those remarks. Santorum (like Trump) is free to do so, but declines. We are free to think less of Trump for not criticizing bigoted remarks (which they were), and to think less of Santorum for not criticizing Trump's silence. The point of debate is to arrive at the truth, so of course people should challenge falsehoods. Santorum is evading the question of whether the remarks in question were offensive to American Muslims, using "right to their opinion" and "not my job to police civility" rhetoric.
(The list above is not intended to be a comprehensive record of all relevant examples.)