As @stevengj mentioned in a similar thread
The Zlib project makes a good effort at backwards compatibility (using version scripts, if anyone is interested) so it should be safe to force Julia to use a newer version. Does PyPlot work for you if you start Julia as follows?
LD_PRELOAD=${HOME}/.julia/v0.5/Conda/deps/usr/lib/libz.so julia
You can also try setting LD_LIBRARY_PATH to the Conda lib directory, but that exposes your Julia process to other crocodiles in the Python dependency swamp.