I am not so sure that the talk of denying someone's 1st Amendment Rights applies in these cases where one group delibertly sets out to disrupt a political rally of another group.
The Bill of Rights protects Citizens form Government oppression. We have a Civil Court System that gives Citizens recourse against misconduct between each other.
If the conduct progresses to physical violence, then there are criminal laws on the books covering that.
When you decide to have a public event, such as a political rally, you are at the mercy of the crowd. You take a chance that those there will agree with you. If they don't, and verbally disrupt the entire proceeding, your only recourse is to let them have their say, or just shut it down.
Yes, you can have people physically removed, but you are on thin ice if they are private guards as opposed to certified peace officers (police), of some government entity.
Of course, the protesters are walking a Fine line as well. Their actions just might solidify the support of the person that they wish to vilify to an even greater extent, negating their efforts.