Most authors of time-travel stories don’t think out what the implications are of the possibility of going back in past to change the future and/or how that works and what sorts of effects it would have and what it means about the nature of the universe.
The idea of going back in time to change the future/past has massive implications, many of them seemingly paradoxical, and having all sorts of complex implications related to relativity, physics, and the nature of the universe. And even ignoring all that, there is a further insanity-inducing rabbit hole of thought just involving the logical extension that if someone in the future can do that, then a nearly infinite number of other people could theoretically also do that. As soon as you think “oh what a great thing if I could go back in time and change history”, consider that an unlimited number of future meddlers might choose to do something like that for different reasons, some of which might well accidentally make you never have existed, etc. It creates a situation of infinite complexity and zero security, at which point the huge paradoxes start to be comforting, at least to me.
Going back to prevent Jesus’ crucifixion is an even more peculiar notion, since if you think he had something to do with divine super-powers, then he probably doesn’t need your technological parlor tricks, and you’d just be trying to mess with God’s plan, except you’d be part of God’s plan, since everything is, so hopefully he’d at least tell you God’s punchline at that point. Supposedly Jesus didn’t really want to avoid crucifixion. If you did talk him out of it, it’d erase most/all of Christian theology (unless he fooled you and snuck back to do it anyway), which would change most of world history for the past 2000 years in unpredictable but huge ways. What would that then do to the future you came from? If cause & effect applies, your future would not be anything like the one you left, and you’d be bringing back an unknown dude into a foreign future that probably gives no poops about the guy, unless he really was the Son of God™, in which case also who knows?
Another possibility is that given you do exist, and maybe cause & effect needs to make sense, you probably can’t change history. If you start to try, something must’ve happened to stop you, or else you wouldn’t exist to change it, so clearly you didn’t. Or you vanish in a puff of logic when you do. Certainly the future you came from does, unless . . .
Another option that could allow all of that would be if when you travel back in time, you actually also travel to another possible history, and the one you came from continues as it was. This tends to strongly imply to me that there are a practically endless variety of possible universes, and so the most you can really do is affect which one your consciousness is on by your choices, including both time travel and mundane choices without time travel. That actually seems relatively plausible to me, but also removes most of the significance of changing world history, since you really don’t – you just get to move to a history where something happened differently, of which there are probably infinite variations, and you vanished from one history where that change didn’t happen.