I have tables with accented letters and other non-roman scripts, but they do not appear inside the environment tabular.
The letters do appear outside of the tabular environment.
i compile with make4ht -ul hello.tex
I use an extension of tex4ht by @michal.h21,
https://github.com/michal-h21/helpers4ht
\documentclass[oneside,a4paper, 12pt]{article}
\usepackage{tabularx}
\usepackage{tabulary}
\usepackage{array}
\usepackage{longtable}
%\usepackage{ragged2e}
%\usepackage{multirow}
%\usepackage[table]{xcolor}
%\usepackage{eqparbox}
%\usepackage{calligra}
%\usepackage{tabu}
\usepackage{alternative4ht}
\altusepackage{fontspec}
\setmainfont{TeX Gyre Termes}
\newfontfamily\greekfont{Linux Libertine O}
\newfontfamily\russianfont{Linux Libertine O}
\newfontfamily\hindifont{Siddhanta}
\altusepackage{polyglossia}
\setmainlanguage{french}
\setotherlanguage{czech}
\setotherlanguage{greek}
\setotherlanguage{russian}
\setotherlanguage{hindi}
%\usepackage{array}
\newcolumntype{Q}{>{\global\let\currentrowstyle\relax}}
\newcolumntype{A}{>{\currentrowstyle}}
\newcommand{\rowstyle}[1]{\gdef\currentrowstyle{#1}%
#1\ignorespaces
}
\begin{document}
Πράγα \qquad Μολδάβα \qquad ústředních \qquad Запад \\
éè©«»€ \qquad युरोप \qquad cœur \qquad ññā āṇ
\vspace{2cm}
\begin{tabular}{Qc Ac Ac Ac}
\rowstyle{\upshape\mdseries}
Πράγα & Μολδάβα & ústředních & Запад \tabularnewline
\hline\rowstyle{\itshape\mdseries}
éè©«»€ & युरोप & cœur & ññā āṇ
\end{tabular}
\newpage
\begin{tabular}{Qc Ac Ac} \hline
\rowstyle{\bfseries}
Heading & Big and & Bold \\ \hline
Meek & mild & entry \\
Meek & mild & entry \\
\rowstyle{\itshape}
Strange & and & italic \\
Meek & mild & entry \\ \hline
\end{tabular}
%%%\begin{tabularx}{\textwidth}{ |X|X|X|X| }
%%% \hline
%%% label 1 & label 2 & label 3 & label 4 \\
%%% \hline
%%% item 1 & item 2 & item 3 & item 4 \\
%%% \hline
%%%\end{tabularx}
%%%
%%%\begin{tabular}{| l | p{9cm} |}
%%%\hline
%%%\textbf{Column Name} & \textbf{Column Description} \\ \hline
%%%Test line 1 & Insert text here (line 1)\\ \hline
%%%Test line 2 & Insert text here (line 2)\\ \hline
%%%Test line 3 & Insert text here (line 3) \\ \hline
%%%\end{tabular}
\end{document}
