Because repeat.tex redefines \repeat which the LaTeX kernel uses in the \loop...\repeat construction and, in order to work as described in plain.tex, it is mandatory that the meaning of \repeat is the same as \fi.
You can modify igo.sty to avoid the problem.
After \input{repeat.tex} add
\let\REPEAT\repeat
\let\repeat\fi
and change all occurrences of \repeat in the code of igo.sty with \REPEAT.
It is also better if you change all the code in the Define size of stones section with
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Define size of stones in text (Nikolai Nemov, from size10.clo)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\AddToHook{cmd/normalsize/after}{\def\stonesize{\igo@fonts{9}}}
\AddToHook{cmd/small/after}{\def\stonesize{\igo@fonts{8}}}
\AddToHook{cmd/footnotesize/after}{\def\stonesize{\igo@fonts{7}}}
\AddToHook{cmd/scriptsize/after}{\def\stonesize{\igo@fonts{6}}}
\AddToHook{cmd/tiny/after}{\def\stonesize{\igo@fonts{5}}}
\AddToHook{cmd/large/after}{\def\stonesize{\igo@fonts{10}}}
\AddToHook{cmd/Large/after}{\def\stonesize{\igo@fonts{11}}}
\AddToHook{cmd/LARGE/after}{\def\stonesize{\igo@fonts{12}}}
\AddToHook{cmd/huge/after}{\def\stonesize{\igo@fonts{15}}}
\AddToHook{cmd/Huge/after}{\def\stonesize{\igo@fonts{20}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
It's good igo.sty is not in TeX Live…
igopackage does not appear to be included in the TeXLive distrubution. Is it available online? If so, where? – Mico Jul 25 '22 at 13:21\end occurred when \ifx on was incompletemessages related to the date macro whenigois loaded, I suspect these are responsible. I'm not sure what the problem is exactly or how it can be solved - the package was last updated 15 years ago so it is not surprising that it does not work perfectly with a recent version of LaTeX. – Marijn Jul 25 '22 at 13:41repeat.texwhich redefines\repeatand breaks so various loops including the babel loop. It also redefines font size commands. I would avoid to use it. – Ulrike Fischer Jul 25 '22 at 14:11