You can remove the impact of the space and rule inserted around the box:

\documentclass{article}
\usepackage{xcolor,array}
\newcommand{\cbox}[1]{{%
\setlength{\fboxsep}{-\fboxrule}% Remove impact of space and rule inserted by box
\fcolorbox{red!80}{yellow}{\strut#1}%
}}
\begin{document}
\begin{tabular}{ l >{\ttfamily} l }
Seq1 & gactttgtggacatcaacgtcggc\cbox{tgc}cccatcgacctcgtgtac \
Seq2 & gactttgtggacatcaacgtcggctgccccatcgacctcgtgtac \
Seq3 & gactttgtggacatcaacgtcggctgccccatcgacctcgtgtac \
& *********************************************
\end{tabular}
\end{document}
You can also set the \fcolorbox in the background by capturing the position of the text (using zref's savepos module) and placing a \phantom element via eso-pic.

\documentclass{article}
\usepackage{xcolor,array,zref-savepos,eso-pic}
\newcounter{cboxcntr}
\newcommand{\cbox}[1]{{%
\stepcounter{cboxcntr}% Allow for unique \cbox
\zsavepos{cbox-\thecboxcntr}% Capture (x,y) coordinate of cbox
#1%
\begingroup
\edef\x{\endgroup\noexpand\AddToShipoutPictureBG{%
\noexpand\AtPageLowerLeft{%
\noexpand\setlength{\noexpand\fboxsep}{.5\noexpand\fboxsep}% Reduce the fbox padding
\noexpand\hspace{\dimexpr\zposx{cbox-\thecboxcntr}sp-\fboxsep-\fboxrule}%
\noexpand\raisebox{\zposy{cbox-\thecboxcntr}sp}{%
\noexpand\fcolorbox{red!80}{yellow}{\noexpand\phantom{\noexpand\ttfamily\noexpand\strut#1}}%
}%
}%
}}\x%
}}
\begin{document}
\begin{tabular}{ l >{\ttfamily} l }
Seq1 & gactttgtggacatcaacgtcggc\cbox{tgc}cccatcgacctcgtgtac \
Seq2 & gactttgtgg\cbox{aca}tcaacgtcggctgccccatcgacctcgtgtac \
Seq3 & gactttgtggacatcaacgtcggctgccccatcgac\cbox{ctcg}tgtac \
& *********************************************
\end{tabular}
\end{document}