Yes, the first Amendment, commonly known as Freedom of Speech, is pretty well respected today. People are free to say or print what they want, and for the most part our country accepts this. The first Amendment also lets people peaceably assemble, prevents the government from interfering with religion, and lets people petition the government. For the most part, all of these are recognized and respected today.
Throughout the history of the United States, the Supreme Court has had many opportunities to address the first amendment. Slowly, over time, the first amendment has been expanded. It's not just freedom of speech. Rather, it's freedom of expression. That can mean the right to wear a particular shirt or express ones self through dance, for example.
The first amendment is not better respected today - not by a long shot. The current societal condition is to keep one's mouth shut unless the comments coming forth are only of a politically correct nature. That is very anti-first amendment. People are too quick to be offended and only resect the first amendment if the words agree with them.
No, the first amendment is not as respected today as it was in years past. This is especially true considering how President-Elect Trump has threatened to curtail the freedom of the press by planning to "open up" libel laws. This would make it easier for him to sue news outlets who he feels have treated him unfairly.