How do I get `\captionof`s to be colored, when in `\makenote`s?

\makenote* redefines \color to do nothing and so the internal code of captions can't change the color. You can use another command but be aware that \makenote* has perhaps a reason for the redefinition: It is quite possible that the blue color leaks out.

\documentclass[]{scrbook}
\usepackage{graphicx}
\usepackage{xcolor}

\usepackage{caption}%
\captionsetup{compatibility=false}%

\usepackage{scrlayer-scrpage}
\usepackage{scrlayer-notecolumn} %must be loaded ``Lastest''
\RedeclareNoteColumn[font = \color{blue}]{marginpar} %default

\let\mycolorcommand\color
\DeclareCaptionFont{bluecaptionfont}{\mycolorcommand{blue}}
\captionsetup{font={bluecaptionfont}, labelfont=bluecaptionfont}

\begin{document}

    here is the main text
    \makenote*{ 
        \includegraphics[width=3cm]{example-grid-100x100pt}
        \captionof{figure}{This should be blue}
    }

    \begin{minipage}{0.5\textwidth}
        \includegraphics[width=8cm]{example-grid-100x100pt}
        \tracingmacros=1 \captionof{figure}{Normal captionof's are blue}
    \end{minipage}

    \makenote*{
        Normal notes are blue
    }
\end{document}

A perhaps safer alternative is to locally redefine \normalcolor. Then caption can't reset the color and the color in the note wins:

\makenote*{ 
    \includegraphics[width=3cm]{example-grid-100x100pt}
    \let\normalcolor\relax
    \captionof{figure}{This should be blue}
}