TeX doesn't hyphenate the first word in a paragraph. You can write a \hspace{0pt} before it, then TeX takes this as first word or use lualatex it hasn't such restriction.
\documentclass{scrbook}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{marginnote}
\usepackage[ngerman]{babel}
\usepackage{ragged2e}
\renewcommand*{\raggedleftmarginnote}{\RaggedLeft}
\renewcommand*{\raggedrightmarginnote}{\RaggedRight}
\newcommand\Marginnote[1]{\marginnote{\hspace{0pt}#1}}
\begin{document}
foo\Marginnote{Mülltonnenentsorgungsprogramm}
\end{document}
or with an up-to-date TeX distribution (2018) one needs only
\listfiles
\documentclass{scrbook}
\usepackage[T1]{fontenc}
\usepackage{marginnote}
\usepackage[ngerman]{babel}
\begin{document}
foo\marginnote{Mülltonnenentsorgungsprogramm}
\end{document}
*File List*
scrbook.cls 2018/03/30 v3.25 KOMA-Script document class (book)
scrkbase.sty 2018/03/30 v3.25 KOMA-Script package (KOMA-Script-dependent bas
ics and keyval usage)
scrbase.sty 2018/03/30 v3.25 KOMA-Script package (KOMA-Script-independent b
asics and keyval usage)
keyval.sty 2014/10/28 v1.15 key=value parser (DPC)
scrlfile.sty 2018/03/30 v3.25 KOMA-Script package (loading files)
tocbasic.sty 2018/03/30 v3.25 KOMA-Script package (handling toc-files)
scrsize11pt.clo 2018/03/30 v3.25 KOMA-Script font size class option (11pt)
typearea.sty 2018/03/30 v3.25 KOMA-Script package (type area)
fontenc.sty
t1enc.def 2017/04/05 v2.0i Standard LaTeX file
marginnote.sty 2018/08/09 v1.4b non floating margin notes for LaTeX
babel.sty 2018/09/02 3.23 The Babel package
ngerman.ldf 2018/03/29 v2.10 German support for babel (post-1996 orthography)
***********
\renewcommand*{\raggedleftmarginnote}{} \renewcommand*{\raggedrightmarginnote}{\Centering}– math Mar 03 '16 at 10:50