They are a simple construction, but I'm not sure I've seen any evidence that their construction is automated.
I'm sure they can't automate shirts because the super cheap ones somehow always are Made in Bangladesh. If they could use less human labor they would make them somewhere else.
I believe socks can be fully automated and are mostly made in china.
There is a startup called Unspun that wants to make many types of clothing production fully automated by weaving the complete end product in place. Similar to how socks are woven today.
The current way to make a "finished" clothing product is called "whole garment knitting". Only two companies make machines that can do this; designing the garments is a pain with the current software stack. Most clothing is "cut and sew" -- you make a simple sheet of knitted material and cut and sew a garment out of that sheet. It is wasteful and heavily reliant on cheap labor.