But it's so much more nuanced than that, and this kind of false dichotomy just polarizes the argument.
Does a right to self-defense mean a right to any and all arms?
Does a right to self-defense mean a right to carry a concealed weapon?
Does a right to self-defense mean a right to carry a weapon in any and all locations?
And that's just the first three questions that sprint to mind.
In fact, you anticipated this with your example of free speech, though probably not in the way you intended. After all, free speech is not an unlimited right. For example, libel and slander laws are on the books to balance free speech rights against the rights of others who might be harmed by that speech.
Why wouldn't you have a similar debate on the balance of harms regarding the right to possess and carry a firearm?
Don't trivialize this. It just makes it an "us-vs-them" conversation, and I think we can all agree there's enough of that already.