I have set Seamonkey as default browser within SM and under preferred applications.
Yet apps that have a help section always use Firefox to go to their help website.
andyk_~/Downloads$ sudo update-alternatives --config x-www-browser
[sudo] password for andy:
There is only one alternative in link group x-www-browser (providing /usr/bin/x-www-browser): /usr/bin/firefox
Nothing to configure.
Can that be stopped ?
Try removing Firefox.
I like using a 2nd browser.
There should be a fix that does not involved doing that.
I agree, I faced similar issues with other distros and browsers too, unfortunately removing the system default browser and sticking with just one browser was the best solution for me, or just using Firefox. Maybe with Ubuntu MATE it will be easier but I have had a hard time time trying to make this work in other distros,end up giving up and used just one browser.
SOLVED 
I kept plugging away and trying different things.
I found a fix.
I used this
gksu synaptic-pkexec
instead of
synaptic-pkexec
Now when I click on Visit homepage within synaptic, it uses Seamonkey instead of Firefox.
I just tested opening websites of packages on Synaptics and I got this error(my default is Chromium)
After that, I tried removing Firefox to try to solve this and nope... Synaptics fails to launch the browser... I click 'visit website' and nothing happens.
Did you set Chromium as your default browser from within Chromium?
And did you use gksu synaptic-pkexec to launch synaptic ?
Also do this substituting Chromium for Seamonkey.
Use the following commands to set up seamonkey as the default browser:
Install it as an alternative browser:
sudo update-alternatives --install /usr/bin/x-www-browser x-www-browser /usr/bin/seamonkey 40
You can verify it's been installed in the alternatives with:
update-alternatives --display x-www-browser
Finally, set the default broswer with:
sudo update-alternatives --config x-www-browser
Chromium was set as the default and on the preffered apps is there too as my default browser.
When I open one of those links from About/help sections they open on Chromium, but Synaptics fails to launch the browser when I click “visit the website”. I tried your command gksu synaptic-pkexec and tried to open any website, it fails again. Looks like it’s a Synaptics issue.
Might want to send a bug report so it can be fixed.
There are a few there already:
https://bugs.launchpad.net/ubuntu/+source/synaptic/+bug/1168915
https://bugs.launchpad.net/ubuntu/+source/synaptic/+bug/1662459