I wondered about the logistics of the linen undershirt for a while, and finally decided that they probably wouldn't waste buttons -- which would have had to have been hand-carved -- on underwear. ;)

And also, since I'm pretty sure that washing was done by bashing clothes with cricket-bat type things, the buttons would have got smashed. For centuries people rarely, if ever, washed their outer clothes since they would either be too delicate or (in the case of wool) take too long to dry, so they wore linen next to their skin as it was easy to wash.