Sounds like domestic terrorism to me. These people need be dealt with promptly and severely. Antics like this will only cause America to rally around President Trump. The First Amendment is not license to interfere with or disrupt events, public or private. It is not license for dissident parties to deny public or private commerce and discourse. The Amendment restricts the government from denying the gathering of the people in public to ask the government to hear their grievance and remedy it. Please note (1) it covers the situation for the relationship between the people and the government. (2) It imposes the condition, "peaceably". It does not give immunity to the Rule of Law to persons to cause disorder and commit violence to disrupt the assembly of other persons in public. It gives no right to anyone to interfere in private events.
Persons who incite or inflict violence, intimidation, assault, battery, disorder or other criminal acts on other citizens are not protected by the First Amendment and need to be arrested, prosecuted, convicted and incarcerated.
The anti-Trump demonstrators that tried blocking access to the inauguration were not acting within their First Amendment rights. These demonstrators were violating the rights of others that want to attend the inauguration. The First Amendment does not give you the right to shutdown access to a public event that others want to attend.
No, the First Amendment does not protect those who block access to the inauguration. If protesters want to demonstrate near the inauguration and related activities, they have every right to do so and exercise their first amendment rights, but there is no part of the Constitution that protects a right to bar others from participating in our government.
People should have a right to be free and do what they want. But that doesn't mean that they have a right to use force to try and control other people. The First Amendment is about the right of free speech, not about the right to control others using force.