unusual extra space after semicolons in math mode using Springer Nature template

Question

For reasons I don't understand, the Springer Nature LaTeX authoring template (available via Overleaf and on Springer Nature's site) causes extra space to be inserted after semicolons in math mode.

For example, the following MWE yields:

\documentclass[sn-mathphys,pdflatex]{sn-jnl}

\begin{document}
\begin{equation}
    (x,y)\quad (x;y)
\end{equation}
\end{document}

Whereas replacing the first line with \documentclass{article} yields the expected spacing:

Is it possible to override this behavior in my document without altering the sn-jnl.cls file directly? In particular, is it possible to do this in a more elegant way than e.g. replacing every instance of ; in my document with {;} or /!/!; ?

Edit: As @egreg points out in his answer, the spacing after the semicolon can be avoided by disabling the loading of the program package. However, this approach somehow causes errors (that are not present when the program package is allowed to load) when using the proof environment:

Second Edit: From the comment of @egreg below, a satisfactory solution is given by placing the following before \begin{document}:

\makeatletter
\disable@package@load{program}{} %prevent program package from loading
\makeatother

\documentclass[sn-mathphys,pdflatex]{sn-jnl} 

\AtBeginDocument{\renewcommand\qedsymbol{\ensuremath{\opensquare}}} %fix class bug with proof environment 

Answer 1

The sn-jnl class loads, for no apparent reason, the package program that does silly settings and is the cause of a lot of problems with the class.

In particular, the package defines the semicolon as math active to produce, in math mode, the standard semicolon as punctuation followed by a thick space.

You can disable loading the package program.

\makeatletter
\disable@package@load{program}{}
\makeatother

\documentclass[sn-mathphys,pdflatex]{sn-jnl}

\begin{document}

\begin{equation}
    (x,y)\quad (x;y)
\end{equation}

\end{document}

Complain with Springer that they should, at least, provide an option for not loading program.