have that offspring they have engaged in child abuse
What the fuck are you even talking about?
This is about incest in general, it doesn't necessarily results in child abuse. For example if two siblings want to fuck and end up having a children, they won't automatically abuse their children. Not only that, but being into one type of incest doesn't mean you are into all types of incest.
It might be more likely for that to happen in a mother/son or father/daughter relation, but that isn't guaranteed either.
Contraceptives aren't 100% affective
And it doesn't matter if it is 100% effective or not, if you use more than one contraceptive method it already gives you something close to 99% success rate. Yes shit might still happen, but it is more likely for you to win the lottery.
and requiring abortions is amoral.
I didn't mention anything about abortions, but either way...
Not necessarily. They fucked up, that is the consequence. And since we are talking about biology here in a way or another, the fetus isn't really alive in the very early stages, so tbh it isn't that much more inhumane than your proposal.
It might also be possible to do exams to check if the child will have any major issues or not before doing anything, as it already is possible in normal circumstances, I'm just not sure how much can be predicted tbh.
if you love someone enough you're willing to commit taboo, you should love someone enough to give up reproducing with them
Now that is just bullshit, incest isn't a thing because of overwhelming love, it is a thing because people either developed a fetish for it or somehow their natural instinct to not fuck their own blood didn't develop properly. The latter can happen if they grow up apart etc.
Besides that, people change over time. They might think like that now, but then later in their life they might not want to be together anymore. Most people that get married end up getting divorced or at least end up with a broken ass relationship, being willing to commit incest doesn't makes them a perfect match for each other.
you can't prove that they always use or don't use contraceptives without constant surveillance by the state
You don't need to prove anything, just put up punishments in case that happens. You can add fines, jailtime and so on.
Yes it would still be bad if it happened, but a few people being irresponsible and fucking things up shouldn't mean punishment for everyone else.
And even with what you proposed, there would still be people who would break the law anyway and end up pregnant sooner or later. So what are you gonna do in this case? Probably the same thing I just suggested above.
The point is that this wouldn't be socially acceptable pretty much anywhere in the world, even in Japan you would get weird looks for fucking your sibling or parents, so might as well keep it hidden from society as a whole, including the government.
Which in turns means, why would anyone even subject themselves to sterilization over something that they need to keep secret anyway?