I took my answer at Big tilde in math mode and made two changes: 1) I changed it from an overstack to an understack; and 2) I increased the vertical stacking gap to \LMpt, which is 1pt scaled to the local mathstyle.
\documentclass{article}
\usepackage{scalerel}[2014/03/10]
\usepackage{stackengine}
\newcommand\reallywidetilde[1]{\ThisStyle{%
\setbox0=\hbox{$\SavedStyle#1$}%
\stackengine{\LMpt}{$\SavedStyle#1$}{%
\stretchto{\scaleto{\SavedStyle\mkern.2mu\sim}{.5467\wd0}}{.7\ht0}%
% .2mu is the kern imbalance when clipping white space
% .5467++++ is \ht/[kerned \wd] aspect ratio for \sim glyph
}{U}{c}{F}{T}{S}%
}}
\def\test#1{$%
\reallywidetilde{#1}\,
\scriptstyle\reallywidetilde{#1}\,
\scriptscriptstyle\reallywidetilde{#1}
$\par}
\parskip 1ex
\begin{document}
$x = \reallywidetilde{(p_1',p_2') \in C}$
$\scriptstyle x = \reallywidetilde{(p_1',p_2') \in C}$
$\scriptscriptstyle x = \reallywidetilde{(p_1',p_2') \in C}$
\end{document}

If, by some chance, you actually wanted the text over the tilde (rather than the tilde under the text), that is also easy:
\documentclass{article}
\usepackage{scalerel}[2014/03/10]
\usepackage{stackengine}
\newcommand\reallywidetilde[1]{\ThisStyle{%
\setbox0=\hbox{$\SavedStyle#1$}%
\stackengine{\LMpt}{%
\stretchto{\scaleto{\SavedStyle\mkern.2mu\sim}{.5467\wd0}}{.7\ht0}%
}{$\SavedStyle#1$%
% .2mu is the kern imbalance when clipping white space
% .5467++++ is \ht/[kerned \wd] aspect ratio for \sim glyph
}{O}{c}{F}{T}{S}%
}}
\def\test#1{$%
\reallywidetilde{#1}\,
\scriptstyle\reallywidetilde{#1}\,
\scriptscriptstyle\reallywidetilde{#1}
$\par}
\parskip 1ex
\begin{document}
$xyz \reallywidetilde{(p_1',p_2') \in C} abc$
$xyz {\scriptstyle\reallywidetilde{(p_1',p_2') \in C}} abc$
$xyz {\scriptscriptstyle\reallywidetilde{(p_1',p_2') \in C}} abc$
\end{document}

\reallywidetildecode in my project for well over a year. While attempting to implement apdflatextolualatexconversion, I've located where the\scaletocommand appears to error with a! Missing number, treated as zero., likely due to afontimplementation issue that I've not properly addressed (e.g.Missing character: There is no ∶ (U+2236) in font mdugmr7t!). As a neophyte to the conversion, any thoughts as to how or what I should look for to help address theMissing numberissue would be appreciated. – RosesBouquet Feb 13 '24 at 00:55\reallywidetildeis\sim. And yet, your error code refers to U+2236, which, the best I can tell, is the "ratio" colon: https://www.compart.com/en/unicode/U+2236. So I really don't have a good understanding of what is happening. – Steven B. Segletes Feb 13 '24 at 01:31