Here's the First Amendment to the United States Constitution:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.Notice how it's all "Congress shall make no law" and says nothing about HSX or the internet? That's because the First Amendment applies to laws made by the United States Government, and not to private corporations.
There are plenty of restrictions on First Amendment rights as well. For example, speech that incites violence, threats of violence and obscene speech do not usually receive any First Amendment protection. Even commercial advertising receives less protection than other speech.
By using HSX, you are agreeing not to do a bunch of stuff. For example, you're agreeing not to make libellous, abusive or hateful posts. Also, you're agreeing not to vicitimise people to their religion, gender, sexual orientation, race, ethnicity, age or disability.
Obviously, being able to express yourself and diversity of opinions is an important part of making a community like HSX a place for people to come and discuss movies. But just as important to the community is participating without feeling victimised.