The title should explain the problem.
\documentclass[justified, symmetric]{tufte-book}
\geometry{paperwidth = 8in, paperheight = 10.5in, right = 2.2in, marginparwidth = 1.5in}
\usepackage{ifthen, lipsum, showframe}
\begin{document}
% ------------------------------
\textbf{\thepage} \marginnote{A margin note} \par
\lipsum[1-5]
\vspace{0.5cm}
\textbf{\thepage} \marginnote{\raggedleft A margin note} \par
\lipsum[6-9]
\vspace{0.6cm}
\textbf{\thepage} \marginnote{\ifthenelse{\isodd{\thepage}}{A margin note}{\raggedleft A margin note}} \par % <---- this note should be on the left side of the margin
\lipsum[6-9]
% ------------------------------
\end{document}
The wrong page numbering also results in a wrong display of the margin note:
To be fair, a simple \clearpage before the third margin note solves the problem, but having to solve things manually is both impractical and annoying.

\thepageis not a reliable way to get the current page number in most situations. See for example https://texfaq.org/FAQ-oddpage, https://texfaq.org/FAQ-wrongpn and https://tex.stackexchange.com/q/473903/35864 and – moewe Feb 28 '19 at 16:56\thepagein a document, latex is not confused, it is just not telling you what you expected it to tell you. Use\pagerefto get a page number. – David Carlisle Feb 28 '19 at 16:59ifoddpagepackage from the first link sounds like it could be what you are looking for. Otherwise\pageref+\labelfrom the second link. – moewe Feb 28 '19 at 17:02\pagerefas the argument of the\isodd{}command? – noibe Feb 28 '19 at 17:03\pagerefshould work in ifthenelse (as I took precautions to make it work) just set a\labelon the page you want to reference, but you may find specific tests like the ifoddpage mentioned above to be easier – David Carlisle Feb 28 '19 at 17:04\pagerefduplicate might not be the best one. – moewe Feb 28 '19 at 17:04