President Trump has proven himself to be strong-willed and very outspoken in his beliefs. It does not seem likely that he will stand by and tolerate continued protests against his administration. It appears he is already assembling resources to crack down on anti-Trump protests, though how they handle it remains to be seen.
The media has covered countless stories of Trump losing his temper with those who don't support him. People rarely change, if this has been his behaviour so far, it will only continue. He is a man of moral ambiguity and it isn't likely that he will respect the rights of the people.
Donald Trump cannot handle criticism. He has shown this very well by taking to Twitter and making remarks toward all those who dare say anything bad about him. He has no filter, and is quick to run his mouth when he is angry. He isn't going to sit back and let people protest him without trying to make them pay for it.
During the campaign for President, Trump had a great deal of protesters. He said that he didn't mind the protesters, even though it later came out that they were sent by Hillary to inject chaos into his campaign. Trump will not be any different during his Presidency. He knows about the First Amendment.