With this, all pages are numbered either odd or even. It's done by adding a hook to the output routines, right after page counting is done. The hook is set with \AtPageCounting, adding another \setcounter{page} here. The advantage of this is, that there is no more of-by-one error.
Of course, having only odd or even page numbers will confuse the heck out of book classes, i.e. with only odd numbers there will never be an empty page before a new chapter and with only even numbers there will be an empty page before all new chapters. But with the option openany this doesn't matter anymore.
With only \AtPageCounting{\stepcounter{page}} all page numbers are odd. By adding the line \AtBeginDocument{\stepcounter{page}} all pages are even numbered.
Caution: this hook is not meant for doing any typesetting! This was not tested and will very likely lead to crazy errors!
And also, caution: there are packages/classes, which change the output routines. With those this may not work. But I tested it with the standard classes, the KomaScript classes and memoir. It works with all of them.
\documentclass[a4paper]{article}
%\documentclass[a4paper]{report}
%\documentclass[a4paper]{book}
%\documentclass[a4paper]{scrartcl}
%\documentclass[a4paper]{scrreprt}
%\documentclass[a4paper]{scrbook}
%\documentclass[a4paper,article]{memoir}
%\documentclass[a4paper]{memoir}
\usepackage{etoolbox}
\makeatletter
% the hook
\newcommand*{\at@page@counting@hook}{}
% insert hook after page counting
\patchcmd{\@outputpage}{\stepcounter{page}}{\stepcounter{page}\at@page@counting@hook}{}{%
\GenericWarning{(preamble)\@spaces\@spaces\@spaces\@spaces}{Package preamble Warning: patching \string\@outputpage\space did not work.}}
% setting the hook
\newcommand*{\AtPageCounting}[1]{%
\def\at@page@counting@hook{#1}%
}
\makeatother
% to step page counter by 2
\AtPageCounting{\stepcounter{page}}
% the above alone leads to only odd page number
% adding this line leads to only even page numbers
%\AtBeginDocument{\stepcounter{page}}
\usepackage{blindtext}
\begin{document}
\tableofcontents
\Blinddocument
\end{document}
\AtBeginShipout{\stepcounter{page}}in the preamble. – Ulrike Fischer Jul 12 '18 at 15:10