Removed ‘\edef\:temp{\the\everymath}\ifx \:temp\empty \:warning{tabular within math?}\fi \let\:@tabular:|=\empty’ to allow dealing with
\documentclass{article}% 
\begin{document} 
 
\catcode‘\:=11 
 
 
\def\fff#1{\immediate 
   \write16{....[#1]..........\the\everymath}% 
%   \write16{....[#1]..........\meaning\a:mth}% 
%  \immediate   \write16{.............\meaning\PicMath }% 
} 
 
\ifx \Configure\UnDef\else 
   \Configure{$}{\PicMath}{\EndPicMath}{} 
\fi 
 
\fff{} 
$A$ 
 
\begin{tabular}{l} 
$C$ 
\begin{tabular}{l}% 
$D$ 
\end{tabular} 
\end{tabular} 
 
 
$ 
\begin{array}{l} 
$C$ 
\begin{tabular}{l}% 
$D$ 
\end{tabular} 
\end{array} 
$ 
 
 
\end{document}