I'd say it depends on what kind of conservative - bigot, capitalist, or both.

Deprogramming a bigot can be done by getting them to interact with and make friends with minorities. On paper this doesn't sound hard, but bigots become that way in the first place because they don't have a healthy and diverse social circle, and you may not be able to just give them one. Hell, depending on how bigoted they are, it may not be responsible or even safe to make anyone else have to deal with interacting with them.

Deprogramming a capitalist has to be done very carefully, but I think for many people there is a lot of common ground that can be reached. I think most people feel the same frustrations that we do, but they've been too indoctrinated by the legacy of McCarthyism to recognize that capitalism is the underlying cause of most of what's wrong with the world today. So you have to be slow and subtle in coaxing them towards this, if you use the words 'capitalism', 'socialism', or 'communism', they will just shut down and stop listening.

I'll never forget when my conservative grandmother watched the primary debates back in 2016 and told me she actually thought Bernie made a lot of good points. And then she went on to vote for Trump in November. And I get why! The one thing Bernie and Trump have in common is that they tell people "I know you're mad at the world today, I'm mad too, and I'm going to fix it instead of leaving this status quo where it is." Even if they're on opposite sides of what they want to do about it, they agree that the world sucks, and that's really all that a lot of people need to hear. Start there, and then guide them towards why the world is screwed up and how exactly we fix it.

I think the best argument you can make is to talk about how the rise of automation is going to shape the future. We are moving towards a world where there will be far fewer jobs that need humans than there are humans who need jobs. A world where robots are gonna do all the work for us ought to be a utopia, leaving us free to enjoy life and follow our passions. But capitalism relies on the assertion that everyone must work for a living or else they starve and die - what happens when there aren't enough jobs to go around? The only way we can solve this is to rethink this premise of capitalism, that everyone must work or die. Automation can only be a utopia in a post-capitalist world, under capitalism it will become a dystopia.

Of course, this only works for people who are not rich enough to support capitalism for entirely self-serving reasons. If you're talking to someone whose job is likely to be automated away in the future, those are the people you have the best chance of reaching. If you're talking to someone who is going to own all the robots, hell they probably know and don't care.