Can you restrict Shoreditch from injecting CSS on Public pages with CiviCRM content?
This is a core issue (not specific to Shoreditch) and there is an issue with some discussion related to it here:


https://lab.civicrm.org/dev/core/issues/378


To tag on to your specific point about Shoreditch's CSS, I have found this to be problematic for the display reasons you mention (conflicts with CSS from the front end theme) but also for performance reasons. On one site I found Google Page Speed Insights showed a very low mobile score (2%) with Shoreditch enabled, and it jumped to a more normal level (87%) as soon as I disabled the Shoreditch CSS.