Well I think this is to do with mixing the relative and absolute. If you hit your thumb with a hammer, it will hurt. And the insight that “cause and effect” are illusory isn’t going to help you there, your thumb will still hurt and the way to avoid getting a hurt thumb when hammering in nails is to make sure you hit the nail instead of your thumb.
Yet, all that is also based on a confused way of looking at the world and understanding yourself and everything else. But that confusion is something that you can’t do anything about by just intellectual understanding. There is something you have to see for yourself. Until you see through it then you have to think in terms of ordinary cause and effect. There are some things that we can see really easily, like the thumb hit by a hammer, and other things that are much harder to see.
For instance if you tell lots of lies, you gradually lose some of your connection with what is true, because when you tell a lie in a convincing way to others, then for a moment you have to believe that lie yourself, enough to say it convincingly. Do that enough and you may no longer be able to tell apart true from fake news, perhaps. Which might then have repercussions back on you, making you vulnerable to falling for delusional ideas that are out of touch with reality.
We can probably all think of a few examples of people who seem to have fallen for that sort of thing. It’s not much different from hitting your thumb with a hammer, but somewhat hidden and not so easy to see.
Well to really understand karma and connections is far more hidden than that.
So, it’s quite like cause and effect as scientists understand it, indeed science is part of it, as that also helps us to understand truth and relate to how thing work, and to align with the way things are rather than a kind of pervasive fake news. In a way the path of the Buddha is to realize that fake news is far more pervasive than we think. Indeed we tell ourselves fake news stories all the time without knowing it.
But dependent origination is like a different way into all that. Seeing how things depend on each other not just as cause and effect, but much more intimately than that. Cause and effect suggests things that are connected together, but separate, one thing causing another, but it’s like the one could exist by itself, it just happened to be caused by the other. E.g. I could have a sore thumb for many reasons. And once I have the sore thumb, then it’s just a “sore thumb” and the hammer no longer has anything to do with it.
Dependent origination is to do with seeing things as far more intimately connected than that. To such an extent that the very idea of cause and effect can eventually break down and be seen through as illusory too. But it doesn’t mean that karma ceases to operate. Indeed the way that Buddhas are able to teach us at all is because of the karmic connection we and they had with each other while they were ordinary beings like ourselves. There is something corresponding to Karma for enlightened beings too, it’s part of the activity of the Buddhas, how it is possible to ask them questions, and for them to give detailed specific teachings that answer to our situation, and so on. So seeing through the illusion of karma - that’s on the absolute level, but on the relative level, Shakyamuni Buddha was still able to continue to teach for many decades after he became enlightened, and we can make a direct connection to his teachings right now, and none of that would be possible without what we see as cause and effect in our way of understanding the world.
Hope that helps, a bit.