If general relativity accounts for a redshift, independent of inflation, how can we still know that inflation is viable? Moreover, how do we differentiate the the gravitational redshift and the cosmological redshift observationally?
The cosmologial redshift only requires expansion, not inflation.
However, given that in all directions the red shift is increasing rather uniformly with distance, expansion seems like the only explanation. To be all gravitational, the objects would need to be uniformly at lower gravitation potential as distance from Earth increases.
See this Stanford link for more infomation: http://einstein.stanford.edu/content/relativity/a11859.html