Generally speaking, you should avoid mixing http and https on the same page, so configuring your FME Server for https would be a good idea (it's a good idea, regardless, actually).
See also https://web.dev/what-is-mixed-content/
@david_r - Thanks for the comment. I do understand what the problem is here and am familiar with Mixed Content. The documentation I've seen for setting up HTTPS looks straight forward, so that was going to be my next step. But the verbiage seemed to suggest that maybe the need for setting this up was uncommon, if not unusual. So that had me thinking: heck, maybe there is way around it... and turned my post into a Hail Mary pass.... Been wanting to do this for some time anyway. So HTTPS, here we come!
@david_r - Thanks for the comment. I do understand what the problem is here and am familiar with Mixed Content. The documentation I've seen for setting up HTTPS looks straight forward, so that was going to be my next step. But the verbiage seemed to suggest that maybe the need for setting this up was uncommon, if not unusual. So that had me thinking: heck, maybe there is way around it... and turned my post into a Hail Mary pass.... Been wanting to do this for some time anyway. So HTTPS, here we come!
Unfortunately configuring Tomcat with a certificate is a bit complicated, which I guess is why the articles tend to be longer than you'd expect. I think that most users didn't see the need for https as most installations are behind the company firewall, but with increasing interaction with e.g. the DMZ (FME Server Apps...) it only makes sense to jump through the hoops.
Just remember that you'll have to redo the setup for each upgrade, as the SSL config isn't part of the backup/restore operation. But if you take some notes on what was done, it should be fairly quick to configure the next time.