Great comments Ben.
There's another great benefit to wearing smarter shirts, and that's that people are more likely to take you seriously and not just see you as a tourist or source of income.
The last time I traveled through India and SE Asia, I wore almost exclusively very light weight long pants and button down shirts I had made for me in India, using exactly the same mostly synthetic fabrics all the locals wear. With custom tailoring, they still cost less than anything off the shelf here, fit absolutely perfectly, looked great, and helped a tremendous amount with blending in.
As for 'performance,' they were as good as anything you'll find in high heat and humidity here, maintained full sun protection when necessary, the shirts having buttons, collars and cuffs could ventilate, and they'd keep bugs off you.
Also, if you are concerned about blending in, aside from skipping T-shirts, don't wear Tevas or any other of those types of footwear.