I trained for a few years in one school, but have since moved away and have been looking for a new place to train (most likely in a different style). I know that there will always be differences in techniques with different instructors, whether it's a different style or not. Is it disrespectful to ask about why they do a technique a certain way, or to note the difference in the way I was taught at my old school? I don't want it to come across like I am questioning the way they do things -- I'm mainly curious about the pros and cons of each approach.
It should be fine to ask why techniques are performed in a particular way. Good practitioners understand why and do more than blindly follow what they have been taught.
Good teachers will be able to tell you why. A poor answer is something like, "our style has always done it this way". Keep in mind you may not have sufficient experience to understand the answer.
Asking why a technique is done a certain way is not the same as asking why style A does something differently from style B. The A v. B question requires knowledge of both A and B. If the teacher does not know both A and B, it is not realistic for them to contrast the two.
Some instructors love to contrast and compare, and some instructors consider it highly disrespectful.
There is an old school mentality from some of the more traditional styles which treat it almost like a religion - mentioning anyone else is considered insulting ("If you want to know more about what they teach, why are you here then?"). I don't find that a particularly healthy space to learn in, but that's how some schools operate.
There's also schools or instructors who love these comparisons because it allows them to point out the context or conditions that shape their art vs. others, or why they consider a particular technique or strategy superior, etc.
Even in those schools though, you have students who take up a lot of class time by ALWAYS asking questions of that sort, in which case, it can be simply disrespectful all around, because it disrupts the flow of class, and, in some cases, can be "justify every little detail before I will try anything out and find out for myself" which... is not how useful learning operates. If you have a lot of comparison questions, they're best kept to after class, or quite honestly, to getting a private training session (people's time is worth money...).