I'll exemplify why "sense of justice" isn't a very correct term: my "strong sense of justice" made me only able to play pokemon with monofairy teams for YEARS
Personal convictions aren't just justice or morals, sometimes it's completely random and weird rules autistic people have and got nothing to do with justice! Sure morals also fall into this many times, but not always and not exclusively
Here's a few other examples:
The plates in the dryer must be organized in a certain way, I'll leave space open while washing dishes so I put them all in the right order
I only like using whatever glass cup I consider the nicest (normally the newest and/or thinner) we have at home
I can only perform some specific activies using my right hand, despite being absolutely 100% possible (and many times easier) to use my left one, for example, using the knife, I'll put the knife in my right hand, cut the food and then put the fork in my right hand again to eat it, I COULD just cut with my left hand or just use the fork with my left, but I can't!
And I'll be really mad whenever someone puts the plates in a different order, or when I'm forced to drink on another glass bc the ones I like are dirty, I get angry! I get angry bc of "drinking in the wrong cup"!