Because a lot of NTs here, including myself, seem to have SJ parents with whom they have had a lot of conflict and problems so i was interested to see if SJs had problems with NTs as parents.
I have/had no real issues with my INTP dad. His sense of humor was embarrassing sometimes (LOADS of bad puns), and even though he's easygoing and friendly 90% of the time, when he gets angry, he's terrifying. That was an issue as a kid - I became the deer in the headlights whenever he was mad. And whenever we'd confront him about it, he'd say things like "All I wanted was an answer to my question! I have a RIGHT to be angry!" (which, I guess, is typical of both our types - you let go of the emotion barrier only to be slammed down, and you feel hurt by that).
I'm intrested in the difference as often the difficulties between NT kids and SJ parents come from the SJs reliance and NTs distrust of authority. So NTs rebel causing their SJ parents grief.
I figured in reversed positions their may be a problem a lack of authority or tradition annoying the SJ. Then again it could make the SJ more open to new things and new ideas making them healthier.
I was a very trustworthy and reliable kid. Often my parents would ENCOURAGE me to go out and have fun and stay up late (which is really funny when you think about it). I was never grounded. They never had to punish me, because for me, the guilt of doing something wrong was enough (the phrase "I'm disappointed in you" was one of the worst things they could say to me).
Many aspects of my relationship with my dad are typical of what you pointed out - almost a reversal. Instead of him making rules for me, I'll make rules for myself. Instead of forcing me to stay home, he'd want me to socialize. For example, here's one interchange we had when I was younger (that REALLY irritated me at the time):
Dad: Hey, do you want to go fishing?
Me: ...Not really. It's hot out, and I'd rather stay inside and read or something.
Dad: *gives me the look*
Me: *continuing to make excuses, without realizing that they're excuses* Nobody else in this house wants to go fishing! I don't even like fishing that much... Why wasn't this planned in advance???
Dad: Oh, c'mon. It'll be fun.
Me: Why do you REALLY want me to go?
Dad: It's out of your comfort zone. It'll be good for you.
Me: *not wanting to displease him; realizing that he's the boss* Oh, fine. Let's go.
Overall, though, we're good friends, and always have been. I remember talking to him about random facts about music and science and math even when I was a little kid. We have similar interests, we understand each other, etc, etc. The times that he annoys me are generally not related to type. And everybody can be annoying sometimes.
EDIT: Just found this quote:
NTP parents may not consistently provide the structured, disciplined environment that SJ children tend to prefer.
Yeah, when I think of my dad, "structured" isn't the first word that comes to mind.

I didn't really have much of a need for it, like pure_mercury said. I pretty much made my structured environment myself. My parents had no say in it.