Basically, because the relative speeds of stars within galaxies are much less than the speed of light.
Imagine a structure with dimension 100,000 light years (about the size of a galaxy). Now suppose the components of that structure move with speeds relative to each other of around 100 km/s (or 0.03% of the speed of light). In the time it takes light to cross the structure (100,000 years of course), the components within it will have moved by just 30 light years (0.03% of the size of the structure).
There would therefore be no significant "blurring" of our snapshot of a galaxy caused by the differing light travel times from its structural components.
The other thing you may have not understood, is that the lives of stars are generally much longer than 100,000 years. So the stars that emit the light on the far side of a galaxy are still in existence 100,000 years later, when their light passes stars that are present at the near side of a galaxy.