I think that those who openly oppose the political party should not be allowed to enter the place where the convention is being held. This would be like having an atheist protesting inside a church.
If they peacefully protest outside the convention, that's fine as long as they don't prevent others from attending.
If they are of that party but opposed to the speaker, then peacefully protesting would also be fine. After all it is their convention too.
To me, if your not a member of that political party, you are trespassing. You see it is the funds from those in that party who rent the place were the convention is being held so if your not invited, you should not be allowed access.
A convention is for the person who has won so why show up at someone's house and be rude. I was particularly upset when the policewoman on stage asked for a moment of silence and there was chanting after a minute that black lives matter. That is not the time or the place. That kind of behavior makes others unsympathetic to your cause. There were others protesting during major speakers including the president. It was infuriating. They should not allowed in at all.
The First Amendment gives all Americans (among other things) freedom of expression and freedom to peacefully assemble. Protests -- whether they're held to gain visibility for a movement or simply to express anger at an aspect of the system -- are one way of exercising both of these freedoms. What better time to get one's voice heard than at a convention? Conventions are held in cities; cities have public areas; protesters exercise their rights in these public areas. To ban protesters would be unconstitutional.
The first amendment grants that all citizens have the right to free speech. The government cannot (or should not be able to) dictate where and how protesters organize. Sure, they are a pain in the butt and they are mistaken a lot of the time, but if we don't let THESE protesters do their thing, WE won't be able to protest when the time comes.
The political process needs to be as transparent as possible and that transparency includes allowing protesters to air their grievances at conventions. Conventions are not a party, delegates attend to make their voice heard by choosing a candidate. Protesters, as long as they are not violent, have the same right to make their voices heard.
Conventions should not be protected from protestors since they are a much needed counter-voice to many issues. Even so, there should be measures in place to protect everyone, such as proper permits, an area for safe protesting and metal detectors for buildings where prominent figures who are speaking may become targets.