We all know how Trump reacts to criticism. His on-going battle with SNL is constantly in the headlines and his Tweets are filled with defensive retaliations to criticism. Either he will learn to live with it or he may try to make it difficult for people to express their opinions.
If you look at the conventions of Trump and Obama you will see a remarkable difference. Any Trump protesters are often attacked either verbally or physically and this is shown on video.Obama's however just get laughed at and treated like a mild nuisance. Many people will be scared of Trump and his administration will probably attack protesters of his actions and administration. Whilst Obama has been accused of some of waging a war on whistle-blowers, Trump's aggressive nature makes some think that he will continue Obama's war.
Emotions ran very high in the 2016 U.S. election and you could argue freedom of speech has never been more clear. People are sharing their opinions, no matter how extreme they are, in great numbers. Far from free speech suffering it may actually help it by having a President who causes emotions to run high.
Trump supports free speech. He wants to put business back to work. He wants to make sure that people are free to criticize global warming if they want to. Trump has made it clear that in his presidency, a person can love anyone that they choose. Free speech will grow under Trump, not suffer.