I had to comment out \usepackage[T1]{fontenc} when running tex4ht to bypass an issue why-tex4ht-do-not-change-font-size-of-verb-when-including-usepackaget1font but now I find a strange side effect for not inlcuding this package, which is tex4ht changes \_ in math mode to X in the HTML !
This is auto-generated by Maple. So I am forced now to use \usepackage[T1]{fontenc}
Is there a reason why tex4ht changes \_ to X when not including \usepackage[T1]{fontenc}
PDF has no problem, it is only tex4ht. Here is MWE
\documentclass[11pt]{article}
\ifdefined\HCode
\usepackage[utf8]{luainputenc}
%\usepackage[T1]{fontenc} %do not use. Make tex4ht \verb not accept different fonts
\else
\usepackage{fontspec}
\fi
\usepackage{amsmath,mathtools}
\begin{document}
\[
y = \_C1
\]
\end{document}
Compiled using make4ht --lua -u foo.tex and this is the output

While lualatex foo.tex gives PDF

Question is: Must one include \usepackage[T1]{fontenc} for tex4ht to give correct outpout? only reason I do not include is to due to the font issue size I linked to above, else I would just include it. And is this is what tex4ht should do? Why it works ok with pdf?
ps. At first I thought it was the \it which causes this, but now I see it is the \_ so I edited the question slightly.

\_is processed in your test file, eventually\a:HCharis used, which expands tox. This has nothing to do with\it; try with\[\_y={\it \_C1}\]and you'll get an x in front of y as well; curiously, not with$\_y={\it \_C1}$– egreg Jul 27 '16 at 20:47