When two of my female friends and I spent a month working in a rural hospital in India, we all went out and bought salwar kameez (tunics and loose trousers).
Not only was this for modesty, but simply because where were were going was very rural, and no-one wore western dress (unlike Delhi and Mumbai, where we wore our own clothes).
Basically, no one where we were thought anything of us wearing traditional costume, because it hadn’t occurred to them we would wear anything else (and the nurses and teachers greatly enjoyed dressing us up in their saris for Independence day).
In fact, when we showed them some photos of us with our families, most people were shocked that we didn’t wear salwar kameez at home, and commented on how much nicer we looked wearing them!
So, although I wouldn’t have worn my “outfits” in the parts of India where western clothing (and western women) don’t draw crowds, when you’re in a place where you’re the only real-life white person anyone has ever sen, and a small crowd follows you everywhere you go, wearing not wearing clothing they considered outlandish and immodest was an advantage!