The nuts and bolts:
In[1]:= Precedence[Postfix] Out[1]= 70. In[2]:= Precedence[ReplaceAll] Out[2]= 110.
Thank you to both of you for your prompt answers.
Hi Philip,
As Claudio mentioned, you need to use parenthesis to override the default precedence. /. has a higher precedence than //. The precedence of all operators is documented here.
/.
//
If you put parentheses to stipulate the order of operations this works.
("fish" // Characters) /. {"f" -> "d"}
(* {"d", "i", "s", "h"} *)