Lol and how did you know they were conservative parents? They came to a NY public school in their matching family MAGA hats?
Anecdotally, I'm in a strong Republican area and I see a ton of this. I'd be shocked if the teachers I know who work in Republican dominated areas don't see it as well.
I don't have any nationwide statistics, but the attitude in the cartoon fits far better with a Republican mindset than a Democrat one. Look at the current Republican President and his party. Blaming others for their own mistakes is rife among them, far more so than the Democrats. The Right as a whole is also far more likely to make decisions based on emotions over facts as well, which I'd imagine would line up with blaming others for their children's actions. Law and order is obviously far stronger point for the Left over the Right as well, and that's something that started way before trump ever came into the picture, which you would assume goes with a respect for rightful authority. So unless you have some sort of statistics about it then I don't see any reason why you'd associate that behavior with the Left over the Right.
It could be an odd bipartisan issue, like the anti-vaxers. Where you get the extremes from both sides. But the more I think about it the more likely it would tie in with the modern day conservative mindset. 20+ years ago I think you would have an argument for the Right being 'better' on this issue, but not any more. Tough to say when exactly the switch happened, but I see the Trump era as more of a result of a trend rather than a switch.