ampersand "&" causes if-else-fi to fail

Note that in your actual MWA (I like that! :-D) you are getting

which probably isn't the intended result. The reason behind it is the same as the reason why your first solution fails: cells are groups, and your \def\@ldap is restricted to the fourth column. You should use \gdefinstead to have it working.

Personally I see no point in avoiding the double \if at all costs but this would be a possible way

\newcommand{\admin}[4][]{%
  #2&#3&%
  \def\@rzid{#4}\ifx\@rzid\@empty\relax ./. \else \@rzid\fi &
  \def\@ldap{#1}%
  \ifx\@ldap\@empty\relax % I prefer \if\relax\detokenize{#1}\relax
     \def\@tempa{\textcolor{green}{\ding{51}}&}%
  \else
     \def\@tempa{&\textcolor{red}{\ding{55}}}%
  \fi
  \@tempa
  \\
}

Basically, the \if just sets the definition of\@tempa, which is expanded only after the \if has been worked out.

Conditionals cannot straddle alignment cells, but you can remove the conditional before issuing &; the technique uses \@firstoftwo and \@secondoftwo. See Why the \expandafter\@firstoftwo idiom?

\documentclass{article}

\makeatletter

\newcommand{\admin}[4][]{%
  #2&#3&%
  \if\relax\detokenize{#4}\relax
    ./.%
  \else
    #4%
  \fi&%
  \if\relax\detokenize{#1}\relax
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
  {Yes}{&No}%
  \\%
}
\makeatother

\begin{document}
  \begin{tabular}{@{}lllcc@{}}
    \hline
    \multicolumn{2}{@{}c}{Anwender}
    & \multicolumn{1}{c}{RZ-ID}
    & \multicolumn{2}{c@{}}{LDAP} \\
    \multicolumn{1}{@{}c}{Vorname}
    & \multicolumn{1}{c}{Nachname}
    &
    & \multicolumn{1}{c}{Yes}
    & \multicolumn{1}{c@{}}{No} \\
    \hline
    \admin{First}{Lastname}{fl19}
    \admin{Some}{Othername}{so97}
    \admin[false]{Not}{Listed}{}
    \hline
  \end{tabular}
\end{document}

I also removed the two auxiliary macros, preferring a different safe test for emptiness.