Selectively turn off hyperref links

Instead of \ref* use \@refstar:

\makeatletter
\let\ref\@refstar
\makeatother

Why? hyperref redefines \ref this way.

\DeclareRobustCommand\ref{\@ifstar\@refstar\T@ref}%

\@ifstar is a LaTeX command which tests if the next character is a *. In this case the * would be gobbled and the first of the following commands will be executed (\@refstar), otherwise the second (\T@ref).

Thus, \ref* is essentially the same as \@refstar und you could use that instead.

If one would like to go deeper: the source code documentation of hyperref (or hyperref.dtx on CTAN or on your local TeX system) tells that \HyRef@StarSetRef belongs to \ref* and would not be linked, and \@refstar is defined this way:

\def\@refstar#1{%
  \HyRef@StarSetRef{#1}\@firstoffive
}

Just for the record, another simple way defined within the hyperref package would be to do the following:

\begin{NoHyper}              %% hyperref hyperlinking disabling environment!
  \begin{equation}
    \label{eq:one}
      e^{i\pi} + 1 = 0
  \end{equation}
\end{NoHyper}

Agreed, this won't disable all the necessary equation hyperlinks in one shot, but if needed a hyperref has already made it available for you, if you don't mind a bit of manual labour.