The danger warnings for cotton can be overstated. In dry, temperate conditions (60s F), when riding at an easy pace, there really is no problem. I have merino, polyester etc, but I also ride in cotton T shirts.
The danger comes when temperatures fall to 40s, with rain and wind, when you find yourself far from home with wet, non-insulating clothing. Even with polyester, I may remove a soaked baselayer after a big climb in winter.