Are there any Linux GUIs that can be controlled via command line? I'm looking for a GUI that I can control via the terminal.  Something where I can input a series of moves into the terminal, such as:

&gt;  e4
&gt;  e5
&gt;  Nf3


...and have the GUI update the board accordingly.

Does anyone know of any program(s) like this?

I can't find anything either on Google or by searching previously asked questions.
Given your stated goal,


  "...a GUI that I can control via the terminal. Something where I can input a series of moves into the terminal,..."


and Student T's comment of


  "I'm not aware for any GUI that also offers command line."


I've tried to find paired items of engines that take command line moves and GUIs that will interact well with these.

Your best bet might be Crafty:
It seems that one can use command lines through “Crafty” [ref. 1] in order to play or analyze a chess game within the GUI of XBoard [ref. 2]  (which can run multiple chess variants, in addition to orthochess) – as in one enters one's moves directly via command line at terminal.

Though a very close second best bet would probably be Sjeng:
Sjeng takes command line moves (very definitely) [ref. 4], plays somewhere in the region of ELO 2500(±) [ref. 5, 6], can interface with XBoard [ref. 5], and supports multiple chess variants.

Arena (GUI) seems to be borderline sometimes.  Some indicate it to be unstable within Wine [ref. 7], some have no problem [ref. 8].

“Command-line-chess” uses a TUI, rather than a GUI, but is at least definitely command line based [ref. 9].  Perhaps one might utilize UTF-8's chess characters as a workaround? [ref. 10]



References:


https://www.cis.uab.edu/hyatt/craftydoc.html 
http://www.delorie.com/gnu/docs/xboard/FAQ.html 
http://www.linuxlinks.com/Software/Games/Board_and_Card_Games/Chess/index.shtml 
http://www.macworld.com/article/1139946/termchess.html 
http://directory.fsf.org/wiki/Sjeng 
https://www.linux.com/news/chess-engines-linux 
http://www.open-aurec.com/wbforum/viewtopic.php?f=2&amp;t=6550 
http://ubuntuforums.org/archive/index.php/t-377613.html 
https://github.com/marcusbuffett/command-line-chess 
https://en.wikipedia.org/wiki/Chess_symbols_in_Unicode