If you have the name of the font you want to use in the LaTeX fragments, have you tried using a LaTeX header at the top of the file, e.g.

#+LaTeX_HEADER:\usepackage{mlmodern}

(Replace mlmodern with whatever typeface you prefer)

If you don’t want your .org file to become too cluttered at the start, you could alternatively use a setup file via #+SETUPFILE: /path/to/setup-file.org – create an org file e.g. setup-file.org, and include a line like

#+LaTeX_HEADER:\usepackage{mlmodern}

or whatever your fixed-pitch/monospace font is supposed to be, as well as all the other options you want to use for LaTeX (like other \usepackage declarations, \newcommand definitions etc.).

I see. What’s the latest version of webkit that doesn’t have this problem? Have you been able to downgrade to it to verify?