You are able to walk through closed double fence gates when they are attached to cobblestone walls or mossy cobblestone walls when they're facing east/west. The point where you walk through is in between the fence gates. Double fence gates seem to work normally when attached to wooden fences though.

gatharian added
Steps to duplicate
-Place down gates and cobblestone wall to form a square. (see photo attached.)
You will be able to walk threw at least one of the gates from a certain side.