A problem with Hebrew and English underlined text

Put the \textenglish{aaa} block inside the same \uline:

\documentclass[a4paper,numbers=noenddot]{scrartcl}
\usepackage{fontspec}
\PassOptionsToPackage{normalem}{ulem}
\usepackage{ulem}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\defaultfontfeatures{Scale=MatchUppercase, Ligatures=TeX}
\newfontfamily\hebrewfont[Script=Hebrew]{David CLM Medium}
\newfontfamily\hebrewfonttt[Script=Hebrew]{Miriam Mono CLM Book}
\newfontfamily\hebrewfontsf[Script=Hebrew]{Miriam CLM Book}

\usepackage{polyglossia}
\setdefaultlanguage{hebrew}
\setotherlanguage[variant=american]{english}

\begin{document}
\uline{אאא \textenglish{aaa}}
\end{document}

I made a handful of other trivial changes, such as removing unsupported Koma options and moving the language variant to the preamble instead of every time you change language. And one noticeable one, which was to scale all the fonts to the same height.