I clicked on the NYT link and wished I hadn’t. I understand where the author is coming from, but ergh, it’s not just about the male gaze. Learn from experience when you expose your chest because your loose shirt snagged on a barbell whilst cleaning; or the barbell pulled your pants down whilst deadlifting; or—my favourite—the treadmill grabbed hold of your pants, leaving you in your knickers (happened to a former housemate). I can’t imagine doing contemporary yoga with its inversions, while having to worry about my part of my body was being exposed. The most compelling counter-argument concerns vaginal health, but I digress.
Have you called any martial arts studios to find out where they get their clothing? The uniforms tend to be loose and allow free movement, so you might to start there if you haven’t found anything.