The videos I make are MP4 and/or MOV files produced using Camtasia 2.
Not a Comasia user, so I am not sure what specifics are offered. Would normally expect the MP4 files to contain "standard" MPEG-4 video (either H.264/MPEG-4 AVC or MPEG-2) with MPEG-4 audio (AAC) encoded data. Since the MOV file container is generic, it could contain many different compression formats and you would have to be more specific regarding the content or provide a sample clip for examination.
They get posted to our digital learning environment (we use Blackboard) and if I go there in Safari, I can't load them.
Since you did not provide provide a link to a problem web page (if even available for a guest visit), I went to the main Blackboard site. All of the sample videos I looked at were standard H.264/AAC MP4 files coded to display in everything from "Pepper" plugins to various custom media players used by a number of services like SDL Media, Vimeo, YouTube, etc. Basically, the files used on the main Blackboard site should be playback compatible with any of the "big five" browsers with or without plugins. (I viewed the content using Safari with the QT plugin disabled but El Capitan didn't disable RealPlayer, Shockwave Flash, or Silverlight plugins.)
This brings up the question of whether all of your posted files are unplayable or just some of them. In addition, can you play the video on this web page?:
http://www.blackboard.com/new-learning-experience/index.aspx
or this one?:
http://www.blackboard.com/sites/design/index.html
I am trying to learn if there your problem is associated with the specific content, manner in which pages are coded, alternative system configurations, a possible problem with the Safari/El Capitan software installation or some combination thereof. (E.g., following my installation of El Capitan, Safari worked fine but Firefox behaved in a weird manner until I re-installed it.)
I don't doubt that the age of the website plays a role, but it remains odd that after upgrading, I can't do something I used to be able to do which is frustrating because if I can't view the videos I post, there's a good chance that a lot of students can't either.
I'm not a web programmer, but from what I saw on the main Blackboard site, their coding appears reasonably "up to date" and able to support the latest versions of Safari, Firefox, and Chrome without problem on my system. Of course, I don't know how/who maintains/updates the individual school/university web areas or if the same coding practices are the same in all areas.
I spoke to a service rep yesterday and they have suggested re-installing El Capitan, which I will try, but it's worth noting that when I googled the problem, I found other forums where people were having the same problem, and the consensus on those forums seemed to be that the new Safari is simply not supporting older types of video content anymore, which isn't a problem if you only need up to date sites, but folks working in education, and some other fields, aren't able to upgrade everything so quickly.
My personal experience is somewhat limited, but looking into a problem with what appears to be a Rice University undergraduate multimedia learning site set up in 2003 and later "transplanted" under an NSF grant, it appears that the QT plugin.plugin (which handles QT 7 "legacy" content) is not fully compatible with the latest version of Safari which seems to access QT X AVFoundation playback routines—which may be why the plugin was disabled. In the case of the web site above, media content was compressed as CinePak video with PCM audio in an MOV file container. It appears the plugin accesses the content using the QT plugin specific page code but since the AVFoundation routines don't support playback of this video, the player seems to get stuck in an endless "loading" loop. So, yes, there does appear to be a Safari problem with the "legacy" compression formats which were turned off by default when Lion was released. However, I would have expected your MP4 content to be compatible using the QT plugin and likely without the plugin if the Blackboard page coding is consistent with the coding used on the main web site. The suggestion of re-installing ElCapitan may indicate the service rep feels the content should be playback compatible but some sort of Safari/El Capitan corruption is causing your playback problem. This is why I was wondering if the main web site videos in the links given above are playback compatible with Safari. Another thing you might wish to do is use a different computer updated with El Capitan or try using a different user account on the same computer. If you don't experience the same problem on a different computer, the the problem is localized to your computer, In a similar manner, if a different user account works correctly, then the problem is localized to the specific user account—usually the app PLIST file for that user.