I can't abide by wearing synthetics next to my skin when I hike. I buy second hand, button down cotton lawn shirts that are so light I can easily
take two and rotate them. Light weight woven cotton (such as lawn) dries very quickly. Denser cottons such as chambrays are more difficult, and forget cotton jersey altogether
I work with textiles professionally and am deeply skeptical of any claim that a nylon fabric can facilitate body cooling. Rayon yes- absolutely- but nylon is essentially a plastic... I can't shake the idea of what happens when you leave a bowl of salad wrapped with glad wrap in the sun.
Without doubt the best fibre I've found for hiking is alpaca. Not for shirts, but for socks, gloves, beanies and jumpers. Extremely light, water resistant, and almost incapable of absorbing any smell. I have a daggy, hand knitted alpaca jumper my Mum bought from a market in Peru: it is the garment I would never hike without.