Turn off highlighting (or any package)

You can redefine the commands from the soul package that you use to do nothing.

With highlighting:

\documentclass{article}
\usepackage{color,soul}
\setulcolor{red}
\sethlcolor{blue}
\begin{document}
This is \ul{underlined} and \hl{highlighted} text.
\end{document}

Without highlighting:

\documentclass{article}
\usepackage{color,soul}
\setulcolor{red}
\sethlcolor{blue}
\renewcommand\ul[1]{#1} % <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\renewcommand\hl[1]{#1} % <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\begin{document}
This is \ul{underlined} and \hl{highlighted} text.
\end{document}

You might want to look into the changes packages. By passing it the option final all the markup is suppressed. You can define your own highlights and get a list of changes. This package is design for marking up edits, but you don't have to use it for that.

It has its own tag here.