The solution appears to be described in this post on the thread, synaptic failed to execute default web browser. Input/output error (note that I have modified the links to give clearer contexts and fixed the third broken link):
within synaptic, onClick
handler for the homepage link is
RGPkgDetailsWindow::cbOpenHomepage()
(see rgpkgdetails.cc - Line
201) which calls GetBrowserCommand()
(see rgutils.cc - Line 114)
and invokes /usr/bin/xdg-open
(it is an easily patched shell script)
(see xdg-open.in - Line 432)
if [ -n "$BROWSER" ]; then
open_envvar "$1"
fi
Patching here will guard against anything routed through xdg-open
(not just synaptic)
if [ -n "$BROWSER" ]; then
if [[ $EUID -eq 0 ]]; then
open_envvar "su -c ${SUDO_USER} $1"
else
open_envvar "$1"
fi
fi
The reason behind this is nicely described by this post on the same thread:
The mystery of the observation your are facing is due to security
settings and different users involved.
Background: When you start synaptic, the GUI-app is run as user root.
The problem: When you click on a link to open a web-browser, synaptic
forwards the call to open a webbrowser as user root. This has certain
system-security and stability related implications.
Further : Synaptic can be started in different ways to run as user
root, those different calls do have different system-security related
constrains. (It can be called either via pkexec, gksu or gksudo,
depending how the synaptic call is initiated, e.g from the menu, from
MX-updater or something else.) Setting the default browser, within
preferred applications or the through the debians alternative
mechanism, is not sorting the issue provided by those
security-constrains.
Summary: As it is now the simplest way would be the copy the link and
open the browser manually. This needs to get further considerations to
provide a stable and secure way of calling from a GUI-app (running as
user root) the users web-browser within the user environment.
This is probably worth noting that the patch could be further modified, as per the final post:
Nice idea to "secure" xdg-open
a bit, probaly also worth to check it for all types of root-app invocations like, su-to-root, gksu, gksudo and pkexec, as we have f.i. in the menu a synapic-pkexec call.