Parenthesise math expression if it contains operator

Here, I search for +, -, \bullet, and \cdot, but you can add more operators to the \setsepchar list.

Also, if the operator is leading, such as -3, I do not add parens. You could change that by commenting the line \ignoreemptyitems.

EDITED to workaround a strange error when \sim appears by itself as an argument to \inlinefrac.

\documentclass{article}
\usepackage{listofitems}
\newcommand\inlinefrac[2]{
  \setsepchar{+||-||\bullet||\cdot||\oplus}
  \ignoreemptyitems
  \readlist*\xator{ #1}
  \ifnum\listlen\xator[]>1\relax(#1)\else{#1}\fi
  /
  \readlist*\xator{ #2}
  \ifnum\listlen\xator[]>1\relax(#2)\else{#2}\fi
}
\begin{document}
\[
  \frac{2}{3}\quad\let\frac\inlinefrac\frac{2}{3}
\]
\[
  \frac{2}{-3}\quad\let\frac\inlinefrac\frac{2}{-3}
\]
\[
  \frac{2+x}{3}\quad\let\frac\inlinefrac\frac{2+x}{3}
\]
\[
  \frac{2\bullet x}{3\cdot y}\quad\inlinefrac{2\bullet x}{3\cdot y}
\]
\centering$\inlinefrac{M\oplus N}{\sim}$
\end{document}

I propose an \ifrac command. If given with * it will call \inlinefrac, but it will also obey the setting done by \fractionsinline (local setting).

This way it's easy to switch from one form to the other, by adding or removing *. You can also use \inlinefrac directly.

Symbols that trigger the parentheses need not be the same in the numerator and the denominator: multiplication symbols should trigger parentheses in the denominator only.

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\ifrac}{smm}
 {
  \IfBooleanTF { #1 }
   { \inlinefrac { #2 } { #3 } }
   {
    \bool_if:NTF \l_bubaya_frac_inline_bool
     {
      \inlinefrac { #2 } { #3 }
     }
     {
      \frac { #2 } { #3 }
     }
   }
 }

\bool_new:N \l_bubaya_frac_inline_bool

% extend the regex at will; \+ and \- stand for + and -,
% \c{command name} for a control sequence
\regex_const:Nn \c_bubaya_frac_num_regex { \+ | \- | \c{sin} | \c{cos} }
\regex_const:Nn \c_bubaya_frac_den_regex { \c{cdot} | \c{times} | \c{bullet} }

\NewDocumentCommand{\fractionsinline}{}
 {
  \bool_set_true:N \l_bubaya_frac_inline_bool
 }

\NewDocumentCommand{\inlinefrac}{mm}
 {
  \regex_match:NnTF \c_bubaya_frac_num_regex { #1 } { (#1) } { #1 }
  /
  \regex_match:NnTF \c_bubaya_frac_num_regex { #2 }
   {
    (#2)
   }
   {
    \regex_match:NnTF \c_bubaya_frac_den_regex { #2 } { (#2) } { #2 }
   }
 }

\ExplSyntaxOff

\begin{document}
\begin{gather*}
  \ifrac{2}{3}\qquad\ifrac*{2}{3}
\\
  \ifrac{2}{-3}\qquad\ifrac*{2}{-3}
\\
  \fractionsinline
  \ifrac{2}{-3}\qquad\ifrac{2}{-3}
\\
  \inlinefrac{2+x}{3}
\\
  \ifrac{\sin x}{x}\qquad\ifrac*{\sin x}{x}
\\
\end{gather*}

\fractionsinline
\begin{gather*}
  \ifrac{2+x}{3}
\\
  \ifrac{2\bullet x}{3\cdot y}
\\
  \ifrac{\sin x}{x}
\end{gather*}

\end{document}