I've always loved classical Indian / eastern / modal sounds on guitar, but I met a man whom I admire that believed that merely copying some of the outward tonalities and calling it "eastern" was disrespectful to the classically trained musicians who were following an art form with a thousand year's worth of tradition and experience.
My question is, how can I learn to properly and respectfully play/learn/interpret eastern music and apply it to the guitar?
With due respect to traditions, you should be free to be inspired by any music. As long as you're not claiming to master that style, I don't think you should limit yourself just because of opinions like those in the question.
Just listening to the music you like, and trying to incorporate those ideas in your music should be fine. To satisfy traditionalists, there is likely no other way than to study with a real master.
The best advice, I suppose, would be to take some sitar lessons. This will teach you what you're dealing with.
You may find that you can't replicate the microtonal Indian scales to an acceptable level using a fretted instrument like a guitar. A slide, bends, alternate tuning might help. You would be trailblazing somewhat. Previous guitar wizards dabbling in Eastern music just used Eastern instruments (for example, George Harrison).
There are some Eastern scales that can be translated into Western notation and can be successful. In these instances, since the scales can be translated verbatim, the only insulting thing about using them would depend on your intent.
That said, there are many other scales with slight microtonal adjustments that don't conform to the equal-tempered system (such as your guitar, or a piano.) Therefore, it is the perception of the action of "shoe-horning" their culture / music through a Western Idiom that may come across as insulting.
If you are truly passionate then there are some ideas that can begin moving the ball along:
Microtonal guitars do exist, so just realize that without utilizing any instruments with microtonal capabilities, you will only be able to represent a small portion of Eastern music in your playing and writing.
Composers all the way back to Mozart have looked to the East for sounds and have used them to different degrees of success in their music.
