I think T/F and J/P are the two preferences which contribute the most towards one's moral outlook. One could argue that S/N affects how open one is to new ideas, and by extension determines how conservative or progressive they are, but I'm not going to explore that further in this post.
Below are attempts to estimate what one's moral outlook might be based on their type.
FJ: "We are one and we all want the same things. What's good for us all is also good for each one of us. There's a right and wrong way to act towards our fellow human beings, although it seems too many are confused about right and wrong and need guidance."
FP: "It's each and every individual with their own needs who matters most. So many people forget this when they act like they know what's best for everyone else. Live and let live."
TJ: "It's the consequences of actions which determine their right and wrong, regardless of how we feel about them. We all need to be held accountable to each other for our actions in order to maintain social stability."
TP: "Morality is a construct decided upon by society to control others, and thus has little intrinsic value. It's the needs of the situation which matters most."
I regard these positions as a hypothetical general rule instead of being true for all FJs, FPs, TJs, and TPs. Disregarding the issue of middle preferences, it's entirely possible to agree with more than one of the above statements, or to disagree with all of them. This post serves mainly to start a discussion.
As for myself, I identify most strongly with the FP and TJ positions, and the least with the FJ position. Using the nu-MBTI of typology forums, I could argue for an FP or TJ typing on the basis of being on the Fi/Te axis, but I'd still show up as a TP for statistical purposes.
I think that TPs, at least for INTP, means something like "Its a set of consistent principles that, applied in a logical framework, sets what should and what should not be done".
Also, I think that I could actually write something for NT->"Its a construct of logical rules that comes from an inteligent analysis to give rational sense in order to achieve progress in the given enviroment". I could write for SJ either, for NF maybe but I couldnt come with anything for SP.
But my main point here is to show that we could actually create many combinations for morality although I wonder which ones would be pretty fake and shallow on the subject, or if it is quite limited. I know that TJ justice is usually measured by results (consequences of action), but that judging only works if the system evaluated is very close to a meritocracy system because it always says that it is either your fault (when things goes downhill) or your merit (when it works). However, a meritocrathic system is more an exception than a rule in the real world (in terms of political debate there is not even a single one system that it is truly merithocratic). Giving a short resume to a very long discussion, meritocrathic systems needs to follow at least all four of these points:
1) No or minimized heritages.
2) Equal opportunities for every person. In political terms, the motto is equal opportunities for every children, which only works if there is a very good free education and health-care system.
3) A system that can have some kind of "armory" or a defense against randomness. The results to be evaluated must be purely from merit and the random factor/distortions must be either minimal or zero.
4) There is controversy on this, but it is very important to state that "input" must equal "output". Most, if not all, merithocrats agrees that no one can produce hundreds or thousands more than the average, so, all these super or ultra rich lacks merit at least partially. This is an important part that nobody, as far as I know, could tackle it and create a system from a completely objective point of view.
Its quite funny to note that there is not a single country in the world, as far as I know, which passes in all of these four at the same time, however most games do. A regular game does provide equal opportunity to every players if anti-cheat is well stablished once they bought the game and the console (or a good PC). It does not have heritages, you dont inherit items from your parents. If you evaluate the average of results in long terms, the downs and ups from randomness tends to be equal and cancel each other(supposing that the further results are mostly or completely independent from the present results). And most developeres wont let the best players to produce hundreds or thousand times the average players at the same time frame (or handle hundreds or thousands of enemies in a row or without dying, they got bots for that), because if they do most of the player base will simply quit and not buy the game again.
In most societies I believe (I live in Brazil so I will speak in brazillian society, although USA and others shouldnt change much), things arent completely meritocrathic. It is usually a middle point between meritocracy and anti-meritocracy (anti-meritocracy is the obedience of some of these 4 points in reversion - the output must be random or the result must be simply from heritage). In regular societies, the heritage is usually unlimited. There are not equal opportunity for every child. The results are subject to external crisis, floating on marketplace demands and a lot of random stuff. There are people winning hundreds or thousands times more than average per year/month.
I did all this meritocracy tour just to state that TJs "justice" and "fairness" will only be truly fair if all these points I made are met (and maybe you will need even more points), which is more an exception than the rule. I can point many fails: A boss that fires a worker that is not showing up because he/she is sick; A boss that fires a worker due to market low demand; Crisis that bankrupt entrepreneurs; Rich people who deserve to have their life and shows off their superiority on poor people when that does come from pure heritage or by simply a series of fortunate events that made them fortunate (or a combination of both); And I could go further and further. Some of these "justices" can be very cruel from the FJs, FPs and ethical standpoint, and pretty unlogical for INTP/TP (the whole judging while there are inconsistency in the judging principles turns it against logic). Cases like when TJ "justice" says that poor people suffering from hunger deserves it (when most of them just had a series of unfortunate events that, guess what, made them unfortunate). I could go on with more examples. In the end, TJ "justice" is applied when it shouldnt be, creating more unfairness than fairness. To be honest, I wonder if some people who uses this TJ justice (actually, more people than just TJs does, and some TJ can become aware of this flaw and change, I believe) actually do care about it being unfair or only cares if it does seem or it is acceptable as fair despite being not.
And I kind of refuted TJ justice in a INTP way (look for principles and look for inconsistency).