It shifts all datapoints equally in the dollar domain, but not in the log domain (hence letting you get rid of the -infinity). Of course it still preserves orderings, but it's a non-linear transformation of the y-axis.
I'd support this sensitivity check, or if just using one value would prefer a larger offset.
(Same caveat: I might have misunderstood log1p)
It's a nonlinear transformation to turn nonlinear totals back into something which is linear, and it does so very well, as you can see by comparing the log graph with an unlogged graph. Again, I'm not seeing what the problem here is. What do you think this changes? Ordering is preserved, zeros are preserved, and dollar amounts become linear which avoids a lot of potential problems with the usual statistical machinery.
http://www.gwern.net/EA%20donations