DiscussionTools uses the ParserAfterTidy hook, which is problematic in the Parsoid read-views context: because this applies pre-cache, it will affect the parsoid output used for VisualEditor/Flow/ContentTranslation and everyone else. So ideally DiscussionTools should apply this transformation *post*cache, but (a) that has performance implications, and (b) the ParserAfterTidy hook as written supplies a Parser $parser argument, and the parser object isn't available post-cache.
We have a longer-term plan to address this (https://www.mediawiki.org/wiki/Parsoid/ParserOutputTransform) but in order to unblock testing and discover more quickly what other unknown-unknowns might block the DiscussionTools-Parsoid-Read-Views work, we propose to introduce a new ParsoidExperimentalDeprecatedPostProcessingHookDoNotUse that Parsoid will apply post-cache (and which does not supply a $parser argument), and tweak DiscussionTools (temporarily!) to implement this hook. That will let us continue our visual diff and other testing in the short term while we build out the ParserOutputTransform framework in core.