New symbol in math mode; add "equal" line below glyph

Weren't for the sharp cuts this seems to do what you need.

\documentclass[11pt]{article}

\usepackage{amsmath}

\makeatletter
\newcommand\ineq{}% for safety
\DeclareRobustCommand{\ineq}{\mathrel{\mathpalette\rance@ineq\relax}}
\newcommand{\rance@ineq}[2]{%
  \vcenter{\hbox{%
    $\m@th#1\mkern1.5mu\underline{\mkern-1.5mu\in\mkern-1.5mu}\mkern1.5mu$%
  }}%
}
\makeatother

\begin{document}

$\subseteq$ $\subset$ $\ineq$ $\in$

$\ineq_{\ineq}$

\end{document}

accents seems to be using definitions in amsmath, you could simply move it to after \usepackage{amsmath} and then your code would work and would generate the required symbols.

However, there is no need for accents for the last symbol which seems to be what you're looking for. \underline{\in} is sufficient.

\documentclass[11pt]{article}


\usepackage{amsmath}

\begin{document}

you could simply use it like so $\underline{\in}$

\end{document}

Here are two variants with stackengine:

\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}

\usepackage{accents}
\usepackage{stackengine}
\newcommand\ineq{\stackMath\mathrel{\stackinset{c}{0.03em}{c}{-1.5ex}{\mathord{\relbar}}{\in}}}
\newcommand\varineq{\stackMath\mathrel{\stackinset{c}{0.03em}{c}{-1.57ex}{\mathord{\relbar}}{\raisebox{0.2ex}{$ \in $}}}}


\begin{document}

 $A\ineq B\subseteq C$

 $A\varineq B\subseteq C$

\end{document}