The problem has to do with the filming, making money off of, and the distribution of the content, in my opinion.
You have to think about the demographic that would spend a lot of time watching this type of content. A lot of people will watch a clip or two of a pedophile being beaten up because fuck yeah, but there has to be a consistent audience to this type of content for them to have a platform. To have followers, to get donations or money, etc.
The monetization of violent content makes it where there's an inherent bias for you to be the judge and jury of someone else's crime, one that you are purposely creating the incentive to have exist to begin with. There's no end objective besides to intentionally spend hours talking to this guy, lure him into a public space, and beat him up in a spot he can't run away from. Only after they're able to asses in person whether or not the pedophile is a threat, of course, because it's a one sided confrontation and an ambush.
The problem isn't the pedophile being beaten up, it's the people behind the camera who do the beating up. 'Objectively', it's a good thing a pedophile is getting beaten up, and if you wanna let out your anger out on someone, it definitely should be on a pedophile. The reality of it is, though, these people should not be beating up random people either way. At least not in America. And then to be rewarded constantly for it with money, praise, attention, etc. They don't care it's pedophiles, though.
It's a way to create a comfortable space for people who want to watch violent crime, but don't want to feel bad for watching it. And to be fair, it's normal to want to feel the satisfaction of seeing someone horrible get what they deserve. These hunters don't do it a few times though, they do it constantly. It's no longer satisfying karma, it's their job. It's their job to intentionally lure people in to hurt them, to brutalize physically weak individuals. It's sick. The pedophiles are sick, and the hunters are sick. Both can be true.
Even with that being said, it's still hard to feel sympathy for the pedophiles. Anyone who knows anyone who was victimized understands the desire. It's just the fact there's no end goal besides pure violence that makes it... worrisome.