classicthesis StrSubstitute and accented character

xstring functions use \edef which means that any commands that do not work by pure expansion are likely to fail. You get the same error with this simplified input

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage{microtype}


\begin{document}
Il modello associa un valore di 
\edef\foo{verità}

ad ogni formula.
\end{document}

You could use

 {\def\protect{\noexpand\protect\noexpand}\StrSubstitute{verità}{x}{y}}

which makes no error, but drops the accent, depending on the actual requirement it is probably easiest to use an expandable string replace function rather than xstring.

this for example replaces x by y while preserving the accented a

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage{microtype}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand\repl{mmm}
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \regex_replace_once:nnN { #2 } { #3 } \l_tmpa_tl
  \tl_use:N \l_tmpa_tl
 }
\ExplSyntaxOff

\begin{document}
Il modello associa un valore di \repl{vxerità}{x}{y}
ad ogni formula.
\end{document}

The problem, as you discovered, is that \StrSubstitute executes \edef on its arguments. However, this can be avoided.

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage[nochapters]{classicthesis}
\usepackage{xstring}

\begin{document}

Il modello associa un valore di
\saveexpandmode\noexpandarg
\StrSubstitute{virità}{i}{e}
\restoreexpandmode\
ad ogni formula.

\bigskip

\saveexpandmode\noexpandarg
\StrSubstitute{viritò}{ò}{à}
\restoreexpandmode\

\end{document}

If you never need other modes (check the manual, section 3.1.1), you can issue \noexpandarg in the preamble and forget about saving and restoring it.

An easier method might be to use an expl3 implementation (currently classicthesis raises an error, which you can safely ignore).

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage[nochapters]{classicthesis}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\xStrSubstitute}{mmmo}
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \tl_replace_all:Nnn \l_tmpa_tl { #2 } { #3 }
  \IfNoValueTF{#4}
   { \tl_use:N \l_tmpa_tl }
   { \tl_set_eq:NN #4 \l_tmpa_tl }
 }
\ExplSyntaxOff

\begin{document}

Il modello associa un valore di
\xStrSubstitute{virità}{i}{e}\
ad ogni formula.

\bigskip

\xStrSubstitute{viritò}{ò}{à}

\end{document}

listofitems to the rescue.

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage[nochapters]{classicthesis}
\usepackage{listofitems}
\newcommand\loiStrSubstitute[3]{%
  \setsepchar{#2}%
  \readlist\mylist{#1}%
  \foreachitem\x\in\mylist{\ifnum\xcnt=1\else#3\fi\x}%
}
\begin{document}
Il modello associa un valore di \loiStrSubstitute{verità}{e}{x}\
ad ogni formula.

\loiStrSubstitute{verità}{à}{x}

\loiStrSubstitute{verititità}{i}{o}
\end{document}

If you need a star version of the macro that only substitutes the first occurrence,

\documentclass[italian]{article}
\usepackage[utf8]{inputenc}
\usepackage[nochapters]{classicthesis}
\usepackage{listofitems}
\makeatletter
\newcommand\loiStrSubstitute{%
  \@ifstar{\loiStrSubstitutefirst}{\loiStrSubstituteall}}
\makeatother
\newcommand\loiStrSubstituteall[3]{%
  \setsepchar{#2}%
  \readlist\mylist{#1}%
  \foreachitem\x\in\mylist{\ifnum\xcnt=1\else#3\fi\x}%
}
\newcommand\loiStrSubstitutefirst[3]{%
  \setsepchar{#2}%
  \readlist\mylist{#1}%
  \foreachitem\x\in\mylist{\ifnum\xcnt=1\else\ifnum\xcnt=2\relax#3\else#2\fi\fi\x}%
}
\begin{document}
Il modello associa un valore di \loiStrSubstitute{verità}{e}{x}\
ad ogni formula.

\loiStrSubstitute{verità}{à}{x}

\loiStrSubstitute{verititità}{i}{o}

\loiStrSubstitute*{verititità}{i}{o}
\end{document}