Knowing that the system as it is now is wrong does not make me an expert on how we could prevent issues. But some people being able to "do a bit of crime" easier is probably better than the human rights violations that are occurring now. And even otherwise, open borders doesn't inherently mean nothing with no one checking people. Just means you can freely travel. But also, Europe doesn't seem to have an issue of people popping cross the border to "do a bit of crime" and go home to get off scott free. Because that's not how borders and laws work.
And human trafficking is a problem with the world as it is currently. So that's not stopping anything. And hell, it makes "illegal" immigrants easier targets of this kind of exploitation. Can't really get much help if you're in the country illegally and your family member is kidnapped.
Who decides if someone's a pedophile or not? How are you going to track that? Force people to take a test or something? Hell, currently we're in a world where queer people, especially trans people, are called "groomers" and "pedophiles" for the sheer act of being trans. So you call people you don't want to come in pedophiles and then they can't come in. Nope, no trans people allowed because we're all "pedophiles" according to the government.
Okay what, you're going to limit it to people who've been convicted of child sex crimes. Well, then they make the existence of people who they don't like count as sex crimes. Again, as is happening to trans people. Existing in public as yourself is a crime so you're charged and treated the same as a pedophile.
So we've already covered why your logic is completely broken and this idea is stupid. But let's push all of that aside. For the sake of argument, best case scenario, we are only talking about actual genuine pedophiles. Have they committed a crime? Are they in prison? Then they're not crossing any borders since they're incarcerated.
What if they haven't committed a crime yet? Well then we'd have no way of knowing they're a pedophile unless they admitted it themselves. And no these people shouldn't be punished just for having those sexual desires. For one, most people are able to control themselves despite sexual urges. Cases of rapes and sexual assault are the result of power dynamics, not random uncontrollable urges. And two, these people should be given help given this could cause genuine mental distress.
What if they've committed a crime but served their time? Well, what justification is there to stop them? What if they harm another child? Well what if they do it in their own country? That's not going to make a difference. And this also goes into the complex issue that is the prison system and how it's largely useless at doing anything other than containing people as a punishment rather than actually attempting to help reform people.
Anyway no, I don't think there's any justification for restricting any kind of "undesirable" from entering a country. Beyond anything else, it just ends up a loophole to punish any group of people you don't like by branding them as that undesirable. Same for every human right. If it doesn't apply to everyone then it applies to no one.
And if you're a special kind of dumbass who'd say "well what about nazis/the kkk/etc", the answer is that ideologies that are inherently intolerant of other people just for existing do not get the benefit of tolerance themselves.