I would like to resolve the infamous warning destination with the same identifier (name{equation.0.1}) has been already used, duplicate ignored in my MWE below.
Reading around this site, the package order seems to be correct. One solution I found was to use hypertexnames=false as an option for hyperref, which indeed fixes the links, but cannot be used in a document with front/main/backmatter, as then the page links are wrong.
\documentclass{article}
\usepackage{amsmath}
\usepackage{hyperref} % don't use hypertexnames=false
\usepackage{cleveref}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{equation}\label{eq:special1}
a = b \tag{*}
\end{equation}
and
\begin{equation}\label{eq:special2}
c = d \tag{**}
\end{equation}
\Cref{eq:special1} and \cref{eq:special2}.
\end{document}