I was in the same boat for a while, so I know exactly where you're coming from.
I was training under my current instructor for 6 years. During that time, a fellow blackbelt started a "sister" school using the same dojang name. Everything was great for a while, but, after some time, my instructor and the blackbelt had a falling out. To this day, I'm not entirely certain on what the reason for it is, but I have my ideas. I do know that it was nothing to do with anything damaging to students or to the dojang at all...it was more of a personal issue.
So the blackbelt persued other types of martial arts all together...actually shunning TKD in the process. He attempted to open several schools prior to the one he has open now, and was met with little success. The school that is open now is doing well, and he appears to be happy teaching his own methods.
Shortly after their falling out, I stopped attending my instructor...mostly because I was 18, had a girlfriend, and wanted to do the party thing, like alot of dumb kids do. I didn't really try to do anything until I saw an ad in the paper for the fellow blackbelt's new school that he had opened (one of the ones that didn't do so well at the time). So I started attending his class...more for the change of direction than anything else. I was tired of being out of shape and wanted to try something new. So I tried it, and I discovered it just wasn't for me.
So now, I've started going back to my first instructor, and things are going great with my training. I'm satisified with my choice, and I feel like I'm getting what I need out of the instruction that I'm receiving.
Was the choice I made disrepectful? At the time when I made it, I really thought it was. I was scared to even look at my 1st instructor. But now, I've come to realize that the whole point of either one of them offering instruction is to provide instruction to those who choose to be instructed.
What I mean by that is that everyone has the freedom of choice to attend whatever school they choose. I chose to try something new and to attend the class instructed by the fellow black belt. I discovered it wasn't what I wanted, so I went back to my first instructor.
To my knowledge, neither person was offended by the choice that I made...and even if they were, then it's not my problem that they're offended by what I choose to learn.
Now, back in the early days of martial arts spreading in the U.S., I could see something like that being considered disrespectful. Back then, it was considered a loyalty issue. But now, since people have realized that cross training in different martial arts leads to greater martial art success, instructors have accepted the fact that you can receive training from several instructors.
Basically, if your instructor cares for your well-being as a martial artist, it shouldn't matter who you train under or with, only that you train.
This, of course, depends greatly on the reason for the falling out, like bluekey mentioned. If the falling out had to do with something that harmed other students or the school, then it would probably be best to keep your distance.
