If all parts of a reference should appear in a specific color, the command \color in a group in conjunction with \hypersetup for linkbordercolor comes into action.
Store the definition of \eqref first in, say, \@msm@th@ref, then use
\begingroup\leavevmode\color{violet}...
\@msm@th@eqref
\endgroup
in a redefined \eqref macro.
This will use violet as color for parentheses, reference value and link.
Another option is to use mathtools and \newtagform, this will change the number of the equation in place however. (This option is not shown here)
(About the usage of \leavevmode see the comment by egreg below. Thanks to him to point to this possible issue).
\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{hyperref}
\makeatletter
\let\@msm@th@eqref\eqref
\renewcommand{\eqref}[1]{%
\begingroup
\leavevmode
\color{violet}%
\hypersetup{linkbordercolor=[named]{violet}}%
\@msm@th@eqref{#1}%
\endgroup
}
\makeatother
\begin{document}
\section{Foo} \label{section::foo}
\begin{equation}
a \equiv a\label{eq::foo}
\end{equation}
See the important \eqref{eq::foo} but look also at \ref{section::foo}
\end{document}

\documentclass{...}and ends with\end{document}that shows the problem. – Alan Munn Nov 13 '17 at 02:35\eqref? – barbara beeton Nov 13 '17 at 03:10