Good question. But note: the right to free speech can be interpreted to mean only that the government shall not undertake measures to limit your free speech. Now suppose that every time you tried to speak, someone else stopped you from doing so -- say, by standing next to you with a bullhorn, or bombing your newspaper, or rioting outside your editorial office when you print a cartoon they don't like. Do you have the "right" to demand that the government protect your free speech?
We certainly feel we have the right to demand that the government protect us from criminals, for example. But should we? Do we have a "right" to pursue our lives unmolested by criminal predators?
Also note that on the "right to bear arms", again, this is a kind of negative limitation on the government, not a positive demand that they provide you with arms to bear. However, if someone tried to take away your guns, you would expect the government to ... well, at least to come and carry away their corpse.
So ... are there any "rights" at all which require that the government do something, as opposed to refrain from doing something?
Sorry -but you got the examples ALL wrong. YOUR rights never place an obligation on another private citizen. You have no right to demand government SILENCE someone else or that would mean claiming YOUR right of free speech is greater than that of someone else. PRIVATE CITIZENS cannot violate your rights listed in the Bill of Rights -ONLY government can!
You misinterpret the Bill of Rights which is NOT an order for government to GIVE you these things but an order FORBIDDING government from INTERFERING with your free exercise of these rights. That's it -it in NO way places an obligation on government to help you exercise them and it NEVER obligates private citizens to do a damn thing to help you exercise them either! Your free speech right means government may not arrest you for what you said. A lot of people don't get that -but that is ALL it means. You can't be arrested for WHAT YOU SAY. But government NEVER has to HELP you say it though! Government has no obligation to provide a platform for you to exercise ANY of your rights, has no obligation to provide an audience for you, has no obligation to prevent someone else from also exercising THEIR rights which would then be a value judgment about which of us has the greater rights, has no obligation to force others to listen to you against their will, no obligation to prevent others from booing you when you speak and may NOT prevent OTHERS from also exercising THEIR free speech rights!
The exceptions to this involve situations where an audience is purposely gathered for the specific purpose of hearing, seeing or witnessing something -and that audience would not otherwise have even been there were it not for that specific reason. For instance -going to a movie, going to a political rally, a football game -ANYTHING where people are ONLY gathering for the specific purpose that event was created. Now if you go to the movies and start talking during the show and won't shut up -government still can't arrest you for it! But the theater owner can legally throw you out because that audience belongs to HIM and no one has the right to prevent an audience from hearing or seeing what they gathered to see and hear! The Supreme Court ruled on that one a long time ago. But government can't arrest that person for WHAT HE SAID. He can stand up there and cuss his head off and he could possibly get arrested for disturbing the peace if he refuses to leave when asked to do so -but he cannot be arrested FOR WHAT HE SAID. That is ALL your free speech rights mean -government can't arrest you for WHAT YOU SAID. But you can get arrested for what you DID if you refuse to leave when asked or create a bigger disturbance. That means those trying to shout down a politician at his/her own rally can -and ARE -legally thrown out. There is no right to prevent others from seeing or hearing what they gathered together to see or hear and it doesn't matter if the audience paid to be there or not. But those who try to shout down a politician can't be arrested for what they SAID. In this country you can only be arrested for ACTIONS that violate the law -not your WORDS. What you DID, not what you SAID. (yes, exception regarding words intended to incite panic or violence that have the potential to cause physical harm to others)
Your examples are all flawed because of a MAJOR underlying flaw in your assumption about what is and is NOT "rights"! PRIVATE CITIZENS can't violate any of the rights listed in the Bill of Rights! Private citizens cannot violate you free speech right, they can't violate your right to bear arms, they can't violate your right of free exercise of your religion etc. They can break the law with regard to your PERSON though -if they take your guns, they are STEALING. If they prevent you from entering a church, they are TRESPASSING. If they follow you around with a bullhorn and use it every time you open your mouth, they are STALKING, HARASSING and DISTURBING THE PEACE. The bullhorn person would be stopped from doing it NOT because he is somehow interfering with your free speech rights somehow -because PEOPLE cannot violate those -only GOVERNMENT can violate these rights. NOT private citizens. The Bill of Rights -in fact the entire Constitution -is an agreement, endowment of certain powers, restrictions of other powers -with GOVERNMENT ONLY. It places NO obligations on anyone as a citizen though! NONE. I have NO obligation to provide or protect your right of free speech. As a private citizen I believe I do have an obligation to demand GOVERNMENT not restrict your free speech rights -but I am not obligated to GIVE you a platform or audience so you can exercise them -and neither is government.
Government doesn't GIVE us our rights because rights are not GIVEN. If a power can GIVE you "rights", it can use the identical power to TAKE them! That would actually make them PRIVILEGES, not rights. We CLAIMED these rights for OURSELVES and then FORBID government from interfering with the exercise of these rights. It is a major distinction and one far too many people fail to understand. Government doesn't GIVE you rights -we CLAIM them. Government is forbidden from interfering with our ability to exercise them -but likewise, government is never obligated to HELP you exercise them either.
Let's move on to health care on this one -another HUGE misconception. All your TRUE rights only involve what YOU do -your ability to TALK, give your OPINION, publish your WRITINGS. Exercise your FAITH, PRAY, ATTEND the organized religion of your choice etc etc etc.
Not a single TRUE right involves the services of another human being -because that would INSTANTLY make that person your SLAVE! You have NO right to the SERVICES of another human being. PERIOD. End of discussion right there. Since you have NO right to services of another human being, government is never obligated to PROVIDE those services to you at a reduced charge or for free. Because insisting government must do this is a demand that government ENSLAVE OTHER CITIZENS for no reason but the fact they chose a different career from YOURS!
Just because people have CHOSEN to over-value this particular service changes nothing -and it IS over-valued. The creation of the artificial over-valuation of some service GUARANTEES you will pay FAR more for it INDIRECTLY than you would EVER agree to do if you just paid for it DIRECTLY! But government itself is assisting in creating that artificial over-valuation! And every demand that government make sure this particular service is GIVEN to you only worsens that over-valuation. In the meantime, these demands are in reality a DEMAND that we PUNISH people who chose certain careers society has decided to over-value. You aren't ENTITLED to the services of another human being and it isn't your RIGHT to demand it anyway. The problem with health care is the artificial over-valuation of this service to the exclusion of all others. With the apparently STUPID notion that it is NECESSARY to see all sorts of doctors in order to LIVE. No, it isn't -and we don't make access to the things that really ARE necessary just to live a "right" anyway! But with health care, only a tiny fraction of the people actually NEED the services of the medical profession in order to live.
Government doesn't GIVE us the things we actually do need to just LIVE -food, protection from the elements in the form of clothing and housing. Able bodied people are expected to PROVIDE that for themselves -and like it or not, the quality of the food we buy, the quality of the clothing and housing we buy is correlated to how much we are WILLING and ABLE to pay for it. Government ONLY assists those who cannot provide these things for themselves -and they aren't GIVEN top drawer food and housing, are they? They are given SUFFICIENT levels. Health care is only a necessity for a small fraction of the people -but those demanding government enslave those who sell this service are PRETENDING it is one we ALL must have just to exist. But it isn't -the vast majority of us could actually survive fine without EVER seeing a doctor. We use the system in the belief it will improve the quality of our life -not to actually KEEP us alive. You aren't ENTITLED to force others to improve the quality of your life and you have no RIGHT to demand government force others to do it. You have a right to PURCHASE the service just as you do any other service whether it is trash collection or that in a beauty salon. YOUR over-valuation of the service is YOUR problem but demand government make it the problem of those who made a career choice to work in it. Even if it means making slaves of them.