AFAIK that is not intended. So there is no font element which could be set or changed by \setkomafont or \addtokomafont, respectively. Both backaddress=underline and subject=underline uses \underline for the rule below the element. I do not know how the thickness of such a rule can be changed.
So the following suggestions are only workarounds, if you really need colored backaddress and/or subject rules in a letter.
To change only the color of the rules, you can redefine \backaddr@format and \subject@format. Both are internal commands, so the redefinitions can break in the future. Additionally they will be overwritten if you set later backaddress=plain, backaddress=underlined, subject=plain or subject=underlined.
\renewcommand{\backaddr@format}[1]{\color{green}\underline{#1}}
\renewcommand{\subject@format}[1]{\color{blue}\underline{\usekomafont{subject}#1}}
Example:
\documentclass[
fromalign = right,
fromrule = aftername,
%backaddress = underlined,% <- default
subject = underlined,
subject = centered,
]{scrlttr2}
\usepackage{xcolor}
\setkomafont{fromrule}{\color{red}}
\setkomafont{fromaddress}{\color{red}\itshape}
\setkomafont{backaddress}{\color{red}}
\setkomafont{lettersubject}{\color{red}}
\makeatletter
\@setplength{fromrulethickness}{2pt}
\@setplength{fromrulewidth}{9cm}
\renewcommand{\backaddr@format}[1]{\color{green}\underline{#1}}
\renewcommand{\subject@format}[1]{\color{blue}\underline{\usekomafont{subject}#1}}
\makeatother
\begin{document}
\setkomavar{fromname}{Max Mustermann}
\setkomavar{fromaddress}{Hauptstr. 1\\ 12345 Musterhausen}
\setkomavar{subject}{Here comes the subject.}
\begin{letter}{Somebody}
\opening{To whom it may concern,}
here comes some text
\closing{Kind regards,}
\end{letter}
\end{document}
Result:

If you want to change the thickness of the lines too, you can use:
\setkomavar{subject}{\setulcolor{blue}\setul{.65ex}{2pt}\ul{Here comes the subject.}}
\setkomavar{backaddress}{\setulcolor{green}\ul{Max Mustermann, Hauptstr. 1, 12345 Musterhausen}}
The both keys backaddress and subject must be set to plain.
Example:
\documentclass[
fromalign = right,
fromrule = aftername,
backaddress = plain,% <- plain
%subject = plain,% <- changed, but plain is default
subject = centered,
]{scrlttr2}
\usepackage{xcolor}
\usepackage{soul}% <- added
\setkomafont{fromrule}{\color{red}}
\setkomafont{fromaddress}{\color{red}\itshape}
\setkomafont{backaddress}{\color{red}}
\setkomafont{lettersubject}{\color{red}}
\makeatletter
\@setplength{fromrulethickness}{2pt}
\@setplength{fromrulewidth}{9cm}
\makeatother
\begin{document}
\setkomavar{fromname}{Max Mustermann}
\setkomavar{fromaddress}{Hauptstr. 1\\ 12345 Musterhausen}
\setkomavar{subject}{\setulcolor{blue}\setul{.65ex}{2pt}\ul{Here comes the subject.}}
\setkomavar{backaddress}{\setulcolor{green}\ul{Max Mustermann, Hauptstr. 1, 12345 Musterhausen}}
\begin{letter}{Somebody}
\opening{To whom it may concern,}
here comes some text
\closing{Kind regards,}
\end{letter}
\end{document}
Result:

\enquote{...}from thecsquotespackage within the subject, I get a runaway argument. Is that a bug incsquotes? – El Cattivo Nov 15 '18 at 15:41