The issue is shown a bit more clearly by:

% pandoc --mathjax -t html  -f latex
\begin{equation*}
[d,\delta]=0.
\end{equation*}
^D
<p><span class="math display">\[=0.\]</span></p>

I think what's happening here is that there's some code in the LaTeX reader's generic environment parser that skips over bracketed optional arguments that some environments have. This is obviously not wanted for the equation* environment! Escaping the square brackets should be a workaround.

More workarounds:

{}[d,\delta]=0

{[d,\delta]}=0

I've modified the title because this isn't specific to HTML output or mathjax.

% pandoc -t native -f latex
\begin{equation*}
[d,\delta]=0.
\end{equation*}
^D
[Para [Math DisplayMath "=0."]]

I would like to provide another example where this happens: In the following table the first entry in the second row (starts with [) is dropped by pandoc while it's present if the file is processed with LaTeX.

\documentclass{article}
\begin{document}
\begin{table}[htb]
  \centering
  \begin{tabular}{|c|c|c|c|c|c|c|}
       $W$      & $N_S$ & $L$  & $L$  & rel. err. & $L$  & rel. err. \\[0mm]
       [$\mu$m] & [-]   & [nH] & [nH] & [\%]      & [nH] & [\%]\\
    \hline\hline
    1.00 & 32 & 0.2871 & 0.293 & 2.06 & 0.294 & 2.40 \\
    2.00 & 32 & 0.2616 & 0.266 & 1.68 & 0.269 & 2.83 \\
  \end{tabular}
\end{table}
\end{document}

Note that the commands \\ and \\* do have an optional argument that in the example is used.