Ibex makes shirts from renewable merino wool (from New Zealand). Ibex clothing is sewn in the USA (only tiny faction of the shirts sold in the US are actually constructed here).
I like merino wool because it keeps you cool in the summer, and unlike cotton or synthetics, merino does not retain odor, and it does not wrinkle.
The polo shirt shown here is available from Amazon.
Another shirt I like is this organic cotton shirt from Nudie Jeans, which is dyed with natural indigo.