Is there X amount of mass shootings that would change gun supporters' minds, or is that the wrong way to think?

Let me turn this around on the OP:

How many people need to die before you’ll support banning alcohol?

Let’s keep this nice and simple and only consider the effects of drunk driving deaths to innocent people (ie not the person who chose to drink and drive). It happens every day - thousands of completely innocent people have been killed by drunk drivers.

Now, banning alcohol wouldn’t completely eliminate the problem, but it would obviously dramatically reduce it. By advocating for the continued legality of alcohol, you are simply accepting that lots of people are going to die that wouldn’t have died if alcohol were prohibited.

Yes, we try to keep drunk driving from happening. We try to keep shootings from happening, too. The reality is that widespread availability of guns and alcohol are both going to lead to a lot of innocent death.

What if I came to you with a news story every time it happened? What if we covered DUI deaths like we do mass shootings? What if I showed you a picture of a cute family every day and say “the 5 year old is dead, the mother is dead, and the father is in critical condition - all because you think alcohol should be legal… how many dead people do we need before you’ll change your mind?”

But you won’t change your mind, because you’ve just accepted that it’s going to happen and you’re okay with that tradeoff. You want to drink, you want alcohol to be available, so you’re okay with accepting that people are going to die because of it. Maybe you yourself have never drank irresponsibly (just as the vast, vast majority of gun owners don’t ever shoot anyone) and so you don’t feel like you’re contributing to the problem, but by advocating for the legality of alcohol, you are condoning a legal state in which people will pay with their lives for your desire for alcohol to be legally available.

How is that any different from gun owners how gun owners who don’t want to ban guns feel?

The difference is simply that you don’t like guns and you do like booze, so it seems obvious that one should be banned and the other allowed, and you can’t understand how people who have the opposite values can possibly be comfortable with all the death that legal guns bring.

Mass shootings are also very salient, whereas drunk driving deaths are routine. We love stories about mass shootings - we watch the news where they recreate the shooting, they bring in psychologists to talk about the motives of the shooter, and they just milk the shit out of it in every way they can. They’re rare and big and spectacular and that makes us react more emotionally to them, and we lose track of how they fit into the world rationally and statistically. It’s similar to plane crashes vs auto crashes - plane crashes are extremely rare and car crashes are constant, but people often become terrified of plane crashes when one happens and don’t care at all when a billion car crashes have happened since the last plane crash.

But imagine a world where the news covered every drunk driving crash like they covered mass shootings. Imagine a world where something around 50% of the American public wants alcohol banned. That would change your perceptions dramatically even though the same number of people were dying.

And in fact, if the media did do this, it would probably dramatically increase the number of prohibitionists. People aren’t good at judging issues purely rationally, weighing the costs and benefits of every decision. They think emotionally, they look for the salient, they’re easily manipulated by what the media chooses to cover. At any time, the media could choose a topic to cover - like drunk driving deaths, or dog attacks, or anything that happens regularly that hardly anyone pays attention to - and just by reporting on these things they can convince people that these things are very real dangers and the sort of thing they should be afraid of in complete disproportion to the actual risk that the public faces.

Since the public loves to consume media about mass shootings, the media gives people what they want, which makes people dramatically overestimate the relative threat and importance of mass shootings as a means of death. This is why you see the focus on these rare but spectacular events rather than the more mundane every day gun homicides, and you get proposals for laws that aren’t sound public policies because they’re trying to ban the salient - say, guns that look scary - rather than the rational. This also means that the fact that drunk driving deaths are so routine, so common, that it’s not worth reporting on any particular one. The more rare and more spectacular something is, the more attention we give to it.

If you were a prohibitionist, every day you could harp on the new slate of drunk driving deaths, focus on the most emotionally charged ones (cute kids dying, for instance), get righteous about how your opponents - people who want to keep these kids dying just so they can get drunk - are awful people. You’d ask “how many more innocent dead people do we need to see before you’ll change your mind?” This is what we see every time there’s a mass shooting.

You’re saying to yourself “I can’t believe gun owners are willing to allow the slaughter to continue just so they can have their guns!” like it’s some rare, incomprehensible behavior, but almost everyone does this exact same thing for multiple issues. Everyone wants things that aren’t really essential to their lives despite the fact that these things statistically are going to result in harm and death to innocent people.

People willing to accept gun deaths to keep gun legal aren’t thinking any differently than you, there are just personal preference, emotional, and salience factors that make you perceive it differently.