In Muay Thai, when throwing a jab with left hand, should person rotate/turn the body and hips? I went to a different school when traveling this weekend, and thats what the coach recommended. I notice some schools are recommending, and other are not. Is there a fundamental rule, or more preferential from athlete? I ask these questions after researching different ideas online, and seeing videos of Muay Thai fights (with athletes doing both methods).
Incorporate both, and everything in between. Think of jabs existing on a spectrum between no rotation to full rotation.
Rotating as you describe provides more power and reach. It also shifts your body into an attitude that is more perpendicular to the opponent, which leaves you more vulnerable to dangerous counters, especially roundhouses or hooks to the torso.
Jabs with no rotation lack reach and power, but take less time to execute. They are necessary when your opponent is close and are useful when pivoting or retreating. They also enable you to retract more quickly into a defensive posture (leaving you less susceptible to counters), provide a means of distracting your opponent, and prepare you more quickly to throw follow-up techniques.
Next time you're training on a bag, throw some short jabs. They will probably feel quite weak. If you never train them, they will remain weak and relatively ineffectual. Doing pushups with your elbows close to your ribcage will help with this. It is also very important to incorporate your legs and hips into these short techniques, even if only minimal rotation is possible. Doing this will help with power, thanks partly to increased torsional rigidity upon impact.
It is good that you are visiting different schools and seeking a variety of advice. Try not to consider different techniques as 'either or' propositions. It is often the case that one technique will have a utility specific to some circumstances, while another iteration of the technique is preferable in others.