The difference is that god is supposedly all good and all powerful. If the barber also possessed those 2 attributes he could make it so that everybody on earth had their hair the way they like it best, all the time. This story does not represent the situation.
"Then do not blame God for allowing these people to continue in their evil ways, when He is constantly inviting them to come and be saved."
This is also false. At most, what "god" is doing (if we pretend he exists), is let preachers do the job HE should be doing, in a very unconvincing way. Plus, following the bible won't heal a diseased man, nor will it protect a girl from being raped.