When it comes to freedom of speech, and the right to assembly, the First Amendment restricts the government’s ability to limit either. Originally this was just a restriction on the Federal government (that Amendment begins with the words “Congress shall make no low”), but has since through the process of selective incorporation, using the parallel due process clauses in the 5th Amendment against the Federal government and in the 14th the state governments (and by extension local governments like counties, cities, towns, etc) one case and one right at a time starting with Gitlow v New York in the 1920s.
Political parties are private organizations. While one can go to court as a civil matter to insist on them abiding by their own published rules, it has NOTHING to do with constitutionally protected freedom of speech, because they are not government bodies or organizations.
One can argue about the rules being too restrictive, but the process for changing that is through whatever procedures are specified in the rules governing that body.
And even were it an issue of freedom of speech, there are still limitations on the speech that is protected. The original standard, the Clear and Present Danger Test offered by Justice Holmes in Schenck v US, has been rolled back quite a bit.
But there is still the “fighting words” doctrine (from Chaplinsky v New Hampshire) and also the notion of the “heckler’s veto” going back to Feiner v New York in the 1950s.
Those who protested at Trump events, which were legitimately private even if he was seeking a public office, could legitimately be removed and even possibly subjected to criminal charges if they continued to disrupt, or if they entered under false pretenses, depending upon what prior notice had been given.
Your freedom of speech does not extend so far as to shouting down someone else at a private event — which a political convention is — if the organizers of that event want you removed, and possibly even prosecuted. And your speech would certainly not be protected by shouting the kind of language that was used at Barbara Boxer and at the Democratic Party Chair in Nevada.
No, I am not a lawyer.
I do teach government, including Advanced Placement (college leve) and we address a lot of these issues.