When traveling to another country I like to try on their local dress, if one is still prevalent in the local culture. For example when traveling to Ukraine I sometimes put on my Vyshivanka, in Central Asia I might put on a tubeteika and in Jerusalem a kippa is more than appropriate.
Would it be disrespectful for a Westerner (who is not Muslim) to wear the thawb/thobe dress in the Arabian peninsula?
Not at all! In fact, we see it as a sign of respect.
It will also help you with the heat! these things are designed for the hellish weather in this desert.
One thing to remember, be sure to use the right name in the right place, for some reason it has many names depending on the place and people might not understand it. The name "Thobe" in the UAE for example is used for ladies dresses, while Kandura anywhere else but the UAE sounds funny.
Finally, thobe is not related to Islam. It's an ancient dress for the Arabs in the peninsula, way before Islam. However, during my visits to many non Arab countries with Muslim population, I noticed that it's used occasionally, especially when attending Friday prayers.
