But otherwise it does? I doubt you mean that, and this is not my main confusion, but just in case.
Consider a Mormon communal worship gathering (in error, Trinity). I’m thinking possibly you are saying this would have no right to exist (I assume this is shorthand for the people involved have no right to gather to behave thusly). So, any advertisement of the meeting could be shredded with impunity, because the advertisement relates to something that isn’t supported by a right. Just on a public board, or anywhere? Would it matter if a legitimate human government legally protected the advertisement?
How does this relate to this quote from Vat2, which needs to be read with the whole document, but it gives the flavor of how I understand it:
Also, this may be relevant, bold added.
Thus speaks Vat2 of its own self. This may be the crux. Anyway, when I read all of DH, it sounds like they might mean that the person who posts the flyer and/or the community it is posted in and/or the group mentioned on the flyer do have rights, and the rights of the latter seem to not be abrogated merely on account of the religion in question. However, the rights are limited by civil order or something.
I don’t think DH means error has rights; I think they mean people have rights. I doubt they are only talking from the perspective of the State, and not what you or I must do or respect, which is why I went with leaving the flyer in place in my earlier post. Rather, I would more expect the American way of thinking to do that. I might guess the American legal way to look at it might be that the State couldn’t rip it down and who cares about what I do to a three cent piece of paper on a kiosk, unless I proceed to wad it up and dump it by a public highway. Of course, if I dump religious trash on someone’s front stoop, that is okay.

(It bugs me because it inevitably blows all over the neighborhood by the time anyone gets home from work).
Your suggestion may be true that because I am a United States citizen, I am misunderstanding DH. I don’t accept the idea that I am putting nationalism over Church. I am deliberately trying to follow the Church, not the principles of the Bill of Rights.