SOS from Texas
A longstanding USA organic-cotton source of genuinely made-in-USA basic tees. The safest recommendation is the undyed, unprinted styles.
Printed or brightly colored pieces need a separate ink and dye review. EU shipping is not clearly stated, so contact them before you count on it.
A US source in the The Second Skin directory. Check that it ships to Europe; where it does not, the directory lists a European alternative alongside it.