You're always limiting the rights of other people, including their right to live, by asserting your rights. The problem is where to draw the line.
I disagree with that thesis entirely.
Their right to live does not mean in any way that I'm required to surrender mine. Just because you might need an organ donation, doesn't confer an obligation upon me to give it to you. The same as the "right to life, liberty, and the pursuit of happiness" doesn't actually guarantee you a job or to be happy ... merely the right to look for it.
I'd say you just confirmed my point. You don't have to surrender your right simply because the papers would be reversed then. Someone shouting that this or that genre of art is disgusting and should be forbidden is attacking a basic right (free speech) of someone else is just like someone shouting that organ donation should be compulsory is attacking a basic right (physical integrity or even your right to live).
Also, you can give someone the right to look for a job or happiness with no feasible way to achieve the goal.
Because, as soon as you start doing the calculus of whose life is more valuable ... you start using the poor as spare parts for the rich.
Sure. Don't we kinda do that already, in economic terms? (poor people's work pays rich people's health care while having (almost) none themselves)
In my opinion, both of your examples are nonsensical and contrived. That isn't about 'offending someone else's sensibilities' .... it's about making your own rights inferior to that of someone else. I don't see any ambiguity in where to draw the line you seem to think is a broad and fuzzy expanse ... your rights can't extend past the security of my own person.
You may redefine the security of your own person to include quite a lot.