How would we tell antimatter galaxies apart? Given that antimatter galaxies are theoretically possible,
how would they be distinguishable from regular matter galaxies?
That is, antimatter is equal in atomic weight and all properties, except for the opposite reverse charge of the particles, identical to regular matter. Hence a star composed of antimatter hydrogen would fuse to anti-helium in an analogous way to our own Sun, and it would emit light and radiation at the same wavelengths as any regular matter star and would cause the same gravitational forces for planetary systems to form as in any other star system.
Hence, what would be a telltale sign if you were observing a galaxy made up entirely of antimatter?
Also, is there any evidence for that half of all galaxies are not made of antimatter -- while general theories currently assume that there is an imbalance of matter over antimatter in the universe, then what is the rationale for not assuming that there is in fact an even balance between the two?
 A: I concur with Count Iblis's answer that if we would detect an uptick in anti-neutrinos when a supernova occurs within said galaxy.
To understand this, let's take the case of what happens in our familiar 'matter' supernova.  When the unfusable core of a star becomes so dense that the inward gravity pressure exceeds the outward electron degeneracy pressure, the whole core goes from normal density to neutron density in one second.  To put this in perspective imagine the mass of the earth being compressed to a sphere no larger than Manhattan and this happens in one second.  This is because when electron degeneracy pressure is breached, the electrons of all the atoms leave their quantum orbitals and go into the nucleus of the atoms where they get absorbed by the protons and become neutrons and emit neutrinos.
$$e^- + p  \rightarrow  n + \nu$$
An enormous amount of neutrinos are released in this way.  The core contains no more individual atoms, just a super dense solid mass of neutrons.  The sudden collapse of the core causes corresponding implosion of the entire star. The outgoing neutrinos collide with the implosion front and all exothermically fusible elements fuse all at once causing the supernova explosion. And indeed scientists have detected dramatic upticks in neutrino detection during the 1987 supernova.
For an anti matter supernova we have :
$e^+ + \bar p  \rightarrow \bar n + \bar\nu$
where $e^+$ is positron, $\bar p$ is anti-proton,
$\bar n$ is anti-neutron, $\bar\nu$ is anti-neutrino.
So if we see a supernova in a galaxy and detect an uptick in anti-neutrinos instead of neutrinos, that is how we would know the supernova is within an anti-matter galaxy.  You may also notice a surge in anti-matter cosmic rays,ie positrons and anti-protons but these would come later due to speed difference.
A: You're right - for isolated galaxies, there is no obvious way of discerning whether they are made of matter or antimatter, since we only observe the light from them. But if there are regions of matter and antimatter in the universe, we would expect to see HUGE amounts of radiation from annihilation at the edges of these regions. But we don't. You could also make the case that galaxies are well-separated in space, and there's not much interaction between them. But there are plenty of observed galaxy collisions even in our own small region of the universe, and even annihilation between dust and antidust in the intergalactic medium would (probably) be observable. 
A: Let's assume that the anti-matter galaxy is well isolated from galaxies consisting of ordinary matter (you could assume that at the boundary the annihilation reactions would have proceeded very fast and matter and anti-matter don't come into contact at the time we see the anti-matter galaxy). Then the telltale sign would come from supernova neutrinos, although at present we can only detect such neutrinos from nearby galaxies.
When the gravitational collapse happens, the electrons of Iron atoms are pushed into the Iron nuclei and all the protons get converted to neutrons leading to an immediate burst of electron neutrino emissions.. In case of a star made out of anti-matter you would have a burst of electron anti-neutrino emissions, and this leads to a different detection signal in detectors on Earth. There are other processes that give rise to both neutrinos and anti-neutrinos, but the entire process is not symmetrical w.r.t. interchanging matter with anti-matter.
