Undocumented incompatibility between changes and siunitx?

changes uses internally the ulem package, and this can't handle complicated macros. You normally should hide them in a \mbox:

\documentclass[]{article}
\usepackage{changes}
\usepackage{siunitx}
\begin{document}
This is a new length of \SI{8}{\meter};
This is a new length of \deleted{\mbox{\SI{8}{\meter}}}.
This is a new length of \replaced{\mbox{\SI{8}{\meter}}}{\mbox{\SI{3}{\meter}}}.
\end{document}

You can provisionally redefine \SI to use \mbox around it.

\documentclass[]{article}
\usepackage{changes}
\usepackage{siunitx}

\ExplSyntaxOn
\RenewDocumentCommand \SI { o m o m } {
 \mbox{
   \bool_set_false:N \l__siunitx_font_set_bool
   \IfNoValueTF {#1}
     { \__siunitx_combined:nnnn { } {#2} {#3} {#4} }
     {
       \keys_set:nn { siunitx } {#1}
       \__siunitx_combined:nnnn {#1} {#2} {#3} {#4}
     }
 }
}
\ExplSyntaxOff


\begin{document}

This is a new length of \SI{8}{\meter};
This is a new length of \deleted{\SI{8}{\meter}}.
This is a new length of \replaced{\SI{8}{\meter}}{\SI{3}{\meter}}.

\end{document}

I'd prefer a changes method that avoids striking out (color would be sufficient).

\documentclass[]{article}
\usepackage{changes}
\usepackage{siunitx}

\setdeletedmarkup{\textcolor{red}{#1}}

\begin{document}

This is a new length of \SI{8}{\meter};
This is a new length of \deleted{\SI{8}{\meter}}.
This is a new length of \replaced{\SI{8}{\meter}}{\SI{3}{\meter}}.

\end{document}