You need to apply lowercase to the strings before you compare, so it needs to be outside any \edef here I have used \pdfstrcmp to avoid having to define additional temp macros, this primitive is also available in other engines than pdftex, as \strcmp.
This finds all but the last as equal
\documentclass{article}%%% Support command %%%\makeatletter\newcommand\compareStrings[2]{%\edef\tempA{\lowercase{\noexpand\ifnum0=\noexpand\pdfstrcmp {\noexpand\zap@space#1 \noexpand\@empty}% {\noexpand\zap@space#2 \noexpand\@empty}%}\relax}%\tempA \expandafter\@firstoftwo \else \expandafter\@secondoftwo \fi}\makeatother%%%%% End support commands %%%%\begin{document}\def\zz{T e sT}0: \compareStrings{tesT}{tesT}{1}{2}1: \compareStrings{test}{tesT}{1}{2}2: \compareStrings{\zz}{tesT}{1}{2}3: \compareStrings{testj}{tesT}{1}{2}\end{document}