How to make cleveref cross-references match a modified equation label style?

In my point of view the easiest (though not most elegant, perhaps) way is to change \creflabelformat for the equation counter as well, applying the \tagform@ macro explicitly for this.

\creflabelformat{equation}{#2\tagform@{#1}#3}

The #2 and #3 are reserved for hyperref targets.

Here's the full code.

\documentclass{article}
\usepackage{amsmath}

\usepackage[capitalise,noabbrev,]{cleveref}


\makeatletter
\def\tagform@#1{\maketag@@@{[\ignorespaces#1\unskip\@@italiccorr]}}

\creflabelformat{equation}{#2\tagform@{#1}#3}

\makeatother





\begin{document}
    \cref{eq1} is fancy
    \begin{equation}\label{eq1}
        a = b
    \end{equation}  
\end{document}

The following solution uses the \newtagform and \usetagform macros of the mathtools package and the \creflabelformat macro of the cleveref package to achieve your formatting objective.

\documentclass{article}

\usepackage{mathtools} % for "\newtagform" macro
\newtagform{brackets}{[}{]}
\usetagform{brackets} % employ square brackets as delimiters around eq. numbers

\usepackage[capitalise,noabbrev]{cleveref}
\creflabelformat{equation}{#2{\upshape[#1]}#3}

\begin{document}
\cref{eq1} is fancy.
\begin{equation}\label{eq1}
        a = b
\end{equation}
\end{document}