Look, I'm with you: I hate it too. The fact that anybody feels uncomfortable stating their thoughts is a threat to freedom of speech. How can we even begin to identify social tensions when only one side is "allowed" to speak? Democracy is built on open debate, which brings to mind that famous quote, "I do not agree with what you have to say, but I'll defend to the death your right to say it." Unpopular opinions are important, and we are killing them off. However, I've noticed a trend: Our country's overuse of political correctness has become your scapegoat. When someone challenges your unpopular opinion, you blame political correctness for what is actually a basic and necessary social concept: disagreement.
When you blame political correctness, you cut the conversation short. Instead of defending your opinion, you are defending your right to state that opinion—a right which I was never challenging in the first place. And by doing so, you distract from the actual topic at hand, robbing the conversation of what could have been an important exchange of ideas. If I seem mad at something you say, please know I'm not mad that you're stating your opinion; I'm mad at the opinion itself. And when I challenge that opinion, I am entitled to free speech just as much as you are. Because freedom of speech includes the freedom to disagree. Just like you are fully entitled to state your opinion, I am fully entitled to state my disagreement.
Blaming political correctness is not supposed to be a catch-all defense for your opinions; it is simply a defense of your right to state the opinion. Just because you have the right to believe what you want does not mean you are immune from the requirement to back up your claim. Next time you say transgender people are gross, I want to hear why you think transgender people are gross, not why you have the right to say transgender people are gross. Next time you tell me that Muslims are dangerous, I'm going to need a better explanation than "that's just my opinion, I'm allowed to say my opinion." There are people out there who genuinely want to understand your point of view, and we can't do that if your only explanation is an allusion to your First Amendment rights. If you are so secure in the validity of your opinions, then please have the confidence to enter a fair contest of ideas. Truth is revealed only when we consider everyone's point of view—which is something we can all work on. I'll try better if you will too.