Some comments and observations:
Some of the columns don't need any automatic line-wrapping; I suggest you use the basic r style for them.
Inform LaTeX where a permissible linebreak is by writing Differential\-Equations.jl.
Use a threeparttable environment to generate well-aligned table footnotes.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\usepackage[table]{xcolor}
\usepackage{array, caption}
\usepackage[flushleft]{threeparttable}
\renewcommand\TPTtagStyle{\textit}
\definecolor{gray1}{RGB}{238,236,225}
\definecolor{gray2}{RGB}{224,224,224}
\definecolor{oran1}{RGB}{255,192,0}
\definecolor{yelw1}{RGB}{255,227,111}
\definecolor{blue1}{RGB}{197,217,241}
\definecolor{gree1}{RGB}{196,215,155}
\definecolor{crea1}{RGB}{252,245,238}
\definecolor{pink1}{RGB}{218,150,148}
\usepackage{tabularx,ragged2e}
\newcolumntype{R}{>{\RaggedLeft\arraybackslash\hspace{0pt}}X}
\newcolumntype{L}{>{\RaggedRight\arraybackslash\hspace{0pt}}X}
\newcommand{\Poor}{\cellcolor{oran1} Poor}
\newcommand{\Fair}{\cellcolor{yelw1} Fair}
\newcommand{\Excellent}{\cellcolor{gree1} Excellent}
\newcommand{\Good}[1]{\cellcolor{blue1} Good #1}
\usepackage{rotating}
\begin{document}
\begin{sidewaystable}
\setlength\extrarowheight{3pt}
\centering
\begin{threeparttable}
\begin{tabularx}{0.9\textwidth}{LrrrRRrR}
\hline
\rowcolor{gray1}
& Matlab & SciPy & deSolve
& Differential\-Equations.jl
& Sundials & Hairer
& ODEPACK\slash Netlib\slash NAG \\
\rowcolor{gray1}
Language & Matlab & Python & R & Julia
& C++ and Fortran & Fortran & Fortran \\
%\hline
Selection of Methods for ODEs & \Fair & \Poor & \Poor & \Excellent &
\Good{(incl. ARKCODE)} & \Good & \Good \\
Efficiency\tnote{a} & \Poor & \Poor & \Poor & \Excellent &
\Good{(incl. ARKCODE)} & \Good & \Good \\
\hline
\end{tabularx}
\medskip
\begin{tablenotes}
\item[a] Whatever.
\end{tablenotes}
\end{threeparttable}
\end{sidewaystable}
\end{document}
Addendum: Instead of setting the contents of the 7 data columns flush-right ( as is done in your code and in the answer above), it may be better to typeset the columns centered.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\usepackage[table]{xcolor}
\usepackage{array, caption}
\usepackage[flushleft]{threeparttable}
\renewcommand\TPTtagStyle{\textit}
\definecolor{gray1}{RGB}{238,236,225}
\definecolor{gray2}{RGB}{224,224,224}
\definecolor{oran1}{RGB}{255,192,0}
\definecolor{yelw1}{RGB}{255,227,111}
\definecolor{blue1}{RGB}{197,217,241}
\definecolor{gree1}{RGB}{196,215,155}
\definecolor{crea1}{RGB}{252,245,238}
\definecolor{pink1}{RGB}{218,150,148}
\usepackage{tabularx,ragged2e}
\newcolumntype{C}{>{\Centering\arraybackslash%
\hspace{0pt}\hsize=0.9\hsize}X}
\newcolumntype{L}{>{\RaggedRight\arraybackslash%
\hspace{0pt}\hsize=1.3\hsize}X}
\newcommand{\Poor}{\cellcolor{oran1} Poor}
\newcommand{\Fair}{\cellcolor{yelw1} Fair}
\newcommand{\Excellent}{\cellcolor{gree1} Excellent}
\newcommand{\Good}[1]{\cellcolor{blue1} Good #1}
\usepackage{rotating}
\begin{document}
\begin{sidewaystable}
\setlength\extrarowheight{3pt}
\setlength\tabcolsep{4pt}
\centering
\begin{threeparttable}
\begin{tabularx}{0.9\textwidth}{ L cccCCcC }
\hline
\rowcolor{gray1}
& Matlab & SciPy & deSolve & Differential\-Equations.jl
& Sundials & Hairer & ODEPACK\slash Netlib\slash NAG \\
\rowcolor{gray1}
Language & Matlab & Python & R & Julia
& C++ and Fortran & Fortran & Fortran \\
%\hline
Selection of Methods for ODEs
& \Fair & \Poor & \Poor & \Excellent
& \Good{(incl. ARKCODE)} & \Good & \Good \\
Efficiency\tnote{a}
& \Poor & \Poor & \Poor & \Excellent
& \Good{(incl. ARKCODE)} & \Good & \Good \\
\hline
\end{tabularx}
\smallskip
\begin{tablenotes}
\item[a] Whatever.
\end{tablenotes}
\end{threeparttable}
\end{sidewaystable}
\end{document}