The problem is that the running heads are set as small caps.
\documentclass{tufte-book}
\title{Non Italic \protect\textit{Italicized} Part Non Italic}
\author[The Tufte-LaTeX Developers]{The Tufte-LaTeX\ Developers}
\publisher{Publisher of This Book}
\usepackage{lipsum}
\begin{document}
\maketitle
Test\clearpage
pages
\end{document}
You'll need to re-define the running head command so that it marks that one is w/in such an environment, then define an emphasis command which checks to see if it's w/in a running head and when it is, applies \textsc --- alternately, Memoir includes a tufte-inspired appearance, it may be better behaved --- it's certainly more thoroughly documented.
Non Italic \textit{Italicized Part} Non Italic