In recent popular culture many social media sites are blocking or even banning users who are activist of unpopular opinions primarily supporting right wing views. It has become a social norm to accuse people who do not accept the use of modern labels such as the official 61 genders in New York. A recent example of this being Twitter drama in which Milo Yianopolas is banned from Twitter for "harassment" after posting a extremely critical review of Leslie Jones who recently starred in the new ghostbusters movie. In his review Milo refers to Leslie as a "attractive black man". Although Milo was extremely rude I believe he has a right to voice is opinions regardless of how offensive they may be.
I disagree with the resolution that political correctness is threatening free speech. As Jim C Hines once said, "But freedom of speech does not mean freedom from responsibility. Nor does freedom of speech obligate me to agree with your words, or to provide them with a platform." meaning that freedom of speech does NOT protect you from saying ignorant or stupid remarks.
Freedom of speech does specifically protect someone's right to say ignorant or stupid remarks. Anyone who speaks is taking responsibility for their words regardless if you agree or not, and the fact that people have the freedom of speech is their platform on which they can say whatever it is they feel so long as it does not create a clear and present danger. But when people begin to be censored because of their ignorant remarks that is when their first amendment rights have been violated. Take for example certain universities across the u.s have banned certain words that may be connected with "microagressions". The fact that we are banning specific words to protect people's feelings is a clear violation of the freedom of speech.