Caption fontsize in a listing using minted

Non-recommended way for this specific documentclass because it handles captions its own way and this way breaks this functionality.

A possible solution since you don't really share what you really expect as output:

documentclass[journal,12pt,onecolumn,draftclsnofoot,]{IEEEtran}
usepackage[usenames, dvipsnames]{color}
usepackage{listing}
usepackage{minted}
usepackage{caption}
captionsetup{font={normalsize}, textfont={sf}, labelfont={bf,sf}}
definecolor{bg}{rgb}{0.95,0.95,0.95}
newminted{pycon}{bgcolor=bg, linenos=true, tabsize=4}

begin{document}

    begin{listing}[]% * for across both columns
        begin{minted}[mathescape, frame=lines, framesep=2mm, fontsize=footnotesize]{pycon} 
        In [1]: %run listing_minted_demo.py
        Hello World!
        x = 3 + 2 
        end{minted}
        captionsetup{font={footnotesize}}
    caption[]{footnotesize Example caption. I'd like the caption AND the label Listing 1 to be footnotesize.}
    %label{mwe}
    end{listing}

end{document}

You can make listing to use the same setup for the caption as figure.

documentclass[journal,12pt,onecolumn,draftclsnofoot]{IEEEtran}
usepackage{listing}    
usepackage[usenames, dvipsnames]{color}

usepackage{minted}
definecolor{bg}{rgb}{0.95,0.95,0.95}

newminted{pycon}{bgcolor=bg, linenos=true, tabsize=4}

makeatletter
let@float@c@listing@caption
makeatother

begin{document}

begin{listing}[htp]% * for across both columns
begin{minted}[mathescape, frame=lines, framesep=2mm, fontsize=footnotesize]{pycon} 
In [1]: %run listing_minted_demo.py
Hello World!
x = 3 + 2 
end{minted}
caption{Example caption. I'd like the caption AND the label Listing 1 to be footnotesize.}
label{mwe}
end{listing}

begin{figure}[htp]
fbox{rule{0pt}{3cm}rule{3cm}{0pt}}
caption{Example caption}
end{figure}

end{document}