I was not initially sure why this is called "1919". The only connection that I could find was that William Allen White is known for having reported from the Versailles Conference of 1919, and his face is predictably repeated thrice, mimicking their stage setup at the time. However, this investigator has learned that this shirt is a homage to a well-known 1919 lithographic Soviet propaganda poster called "Beat the Whites with the Red Wedge". This 2008-2009 tour shirt has a very interesting design. It features the first names of our five guys cleverly melded together into two pseudo-ambigrams consisting of the original duo and their backing band, with their common letters in red. It is also of note that highlighting the difference between "DAN" and "DANNY" produces "NY", which warrants no interpretation.
*Sorry, I couldn't flip 'MART'.
The back reads "They Might Be Giants on Tour 2008-9" in a charming crossword fashion. This shirt is available at the TMBG Merch Store under the name "1919 on Creme", though my shirt as well as what's pictured appear to be white. I suspect that it's an error caused by the subsequent availability of "1919 on Creme Fine Jersey Slim Fit" t-shirt for women that actually does appear to have a creme hue.