Either redefine \@chapter or use a patch in order to modify the code that writes the ToC entry, i.e. \addcontentsline.
report uses
\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\protect\numberline{\thechapter}#1}%
\else
\addcontentsline{toc}{chapter}{#1}%
\fi
so #1 means the optional argument, but #2 is needed here.
The same is basically true for \@sect, which uses #7, which must be replaced by #8.
The code below uses a switch in order to modify the entry:
Say \uselongtitletrue to enable the long titles in the toc but keep the short ones in the header and \uselongtitlefalse in order to use the short ones.
\documentclass[12pt,a4paper]{report}
%\usepackage{../sty/reportpage}
\usepackage{xpatch}
\newif\ifuselongtitle
\uselongtitletrue
\makeatletter
\xpatchcmd{\@chapter}{%
\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\protect\numberline{\thechapter}#1}%
\else
\addcontentsline{toc}{chapter}{#1}%
\fi}{%
\ifnum \c@secnumdepth >\m@ne
\refstepcounter{chapter}%
\typeout{\@chapapp\space\thechapter.}%
\addcontentsline{toc}{chapter}%
{\protect\numberline{\thechapter}\ifuselongtitle#2\else#1\fi}%
\else
\addcontentsline{toc}{chapter}{\ifuselongtitle#2\else#1\fi}%
\fi
}{\typeout{Success}}{\typeout{Failure}}
\xpatchcmd{\@sect}{%
\fi #7%
}{\fi\ifuselongtitle#8\else#7\fi}{}{}
\makeatother
\begin{document}
%\pagestyle{reportpage}
\pagenumbering{roman}
\setcounter{page}{1}
\cleardoublepage
\renewcommand{\baselinestretch}{1.25}
\small\normalsize
\tableofcontents
\renewcommand{\baselinestretch}{1}
\small\normalsize
\cleardoublepage
\pagenumbering{arabic}
\setcounter{page}{1}
\chapter[First Chapter]{The first chapter has a long title that only is shown as the chapters headline}
Some irelevant text.
\section[Foo]{Long foo section}
\subsection[Foo]{Long foo subsection}
\cleardoublepage
more irrelevant text.
\end{document}

report. I'm going to update my example code. – user159521 Mar 30 '18 at 13:41\sectionbut now it is\chapter? – Mar 30 '18 at 13:57memoirclass (which encompasses thebook,reportandarticleclasses) provides for different entries in the ToC, header, and main text. Read chapter 6 "Document divisions" in the manual>texdoc memoir– Peter Wilson Mar 30 '18 at 17:52