Newcommand options and for each

The problem is unrelated to foreach you would see the same from \def\x{1} \case{\x}

You are comparing \ifx 1\x and the tokens 1 and \x are not the same so this is false.

Conversely \case{12} would test \ifx112 which would test 1 and 1 as true and then typeset 2.

You want to do a numeric test not test the unexpanded tokens, so

\documentclass{article}

\newcommand\case[1]{%
\ifcase\numexpr#1\relax
case 0\or
case 1\or
case 2\or
case 3\else
Illegal%
\fi}
\usepackage{tikz}
\begin{document}

\case{1}

\case{12}

\case{3}


\foreach \x in {1,2,3}{\case{\x}}

\end{document}

I can propose a more flexible set of commands.

\documentclass{article}
\usepackage{pgffor}
%\usepackage{xparse} % uncomment if using LaTeX released before 2020-10-01

\ExplSyntaxOn

\NewExpandableDocumentCommand{\checkcases}{mmO{}m}
 {
  \int_case:nnTF { #1 } { #2 } { #3 } { #4 }
 }

\ExplSyntaxOff

\newcommand{\mycaseswitch}[1]{%
  \checkcases{#1}{
    {1}{Case 1}
    {2}{Case 2}
    {3}{Case 3}
    {42}{Ultimate}
  }{Illegal}%
}
\newcommand{\otherswitch}[1]{%
  \checkcases{#1}{
    {-2}{Negative}
    {2}{Positive}
  }[!]{Bad?}%
}

\begin{document}

\mycaseswitch{1}: case 1

\mycaseswitch{2}: case 2

\mycaseswitch{3}: case 3

\mycaseswitch{4}: illegal

\mycaseswitch{42}: Hey!

\foreach \x in {1,2,3}{\mycaseswitch{\x}\par}

\otherswitch{-2}

\otherswitch{2}

\otherswitch{0}

\end{document}

The \checkcases command is just an interface to the internal expl3 function \int_case:nnTF. It has four arguments:

1. the integer to test against the case list;
2. the case list, in the form of pairs {<integer>}{<text>} (no need that the integers are consecutive or start from 0 like for \ifcase); spaces are ignored between pairs;
3. (optional) text to be used after a successful match;
4. text to be used for “no match”.