I have converted my wardrobe to primarily natural fibers over the past couple years.

I do have some outerwear that's polyester still such as a down great-coat.

I have been extremely impressed with Merino wool and 3 of the 4 shirts I own are Merino wool. My only (!) pair of underwear is Merino wool as well. All of my shorts/pants are cotton, including swim trunks. I have a linen shirt for summer wear.

When I'm riding my bicycle in the summer (say 40C / 100F with mid humidity) my linen shirt definitely shows some sweaty patches especially under backpack straps; within a few days it starts to stink. I find myself washing it weekly or more. My Merino underwear doesn't ever really feel or look soaked and doesn't build up a funky smell even over long periods.

I suspect silk would also make excellent underwear but the only ones I've seen online are sized for tiny asian dudes.

For feet I wear zero-drop sandals which are designed for running. In the winter I wear wool socks, either fluffy ones with my sandals (just for warmth) or army surplus ones with army surplus boots.

If I wanted to wear cotton underwear and shirts I would probably own something like 8 pairs of each, plus some more shirts for autumn & winter. I would also have to do laundry weekly. I did something like that previously but am very happy with my current wardrobe.

Previously I've also had all polyester quick-dry type clothing but switched out of an abundance of caution (also perhaps pursuit of quality/style). The quick-dry poly also did a good job preventing sweat build-up.

Bottom line: I'd encourage you to check out Merino wool and linen. If you don't mind artificial fibers single-layer poly can be good as well.