How is MBTI J/P different from Socionics j/p

[Phaedrus]

We do? Well, I don't!

Well, that means that you are uneducated and still have something to learn about the human psyche.

My personal understanding is that conscientious is a trait which is semi-fixed in personality, but that for most people (people with normal psychology, which is the realm to which Big 5 is applied) it is largely learned behavior, not something that results exclusively out of inborn traits: according to many psychologists, most infants are impulsive and low on conscientiousness, and it a a parent's job to teach conscientiousness.

That is totally wrong of course. All of these traits can be observed from infancy, and all of them are basically inborn. If "many psychologists" have the views you are attributing to them here, they too must be educated since they probably are basing their views on totally false premises. They most likely belong to one of the "dynamic" schools of psychology -- those schools that deny the findings of the natural sciences. We know that our basic personality traits, as they are captured and described by the Big Five, are mostly inborn. That fact is not open for discussion; those who deny it should study some neurobiology.

The question is: can a rational person be low on conscientiousness and an irrational person be high on conscientiousness?

What do you mean by "rational person" here? I am a very rational person in my thinking but not as much in my behaviour. And I am of course an irrational type, since I am an ILI. A person with a rational (j) type in Socionics can not be low on conscientiousness, that's impossible. Either the test result is incorrect or the person is mistyped in that case.