Why would enabling a new module result in the majority of modules disabling? On my Drupal Commerce site, I was attempting to add a Commerce Discount-related module that would allow me to specify a discount based on taxonomy term/product category. When I enabled the module however, my site showed that my enabled module count dropped by ~50 modules. Yikes! This included key features of the site, including payment methods (Paypal, FirstData), as well as XML sitemap-related modules. I also received some exception errors related to existing Rules on the site that were related to shipping rules.

I was able to revive through a backup, but had never seen this type of response before. Any ideas?
It appears you're being affected by a known issue that has been resolved in Drupal 8 but still needs to be back ported to Drupal 7. The PHP extension Suhosin causes modules with parentheses in the package name to be disabled. You can edit your Suhosin configuration to remove parentheses from the array index blacklist or, if you're unable to do that in a pinch, you can edit the relevant module files to remove the parentheses from their package names.

More info in the core issue: https://www.drupal.org/node/2665152