Elastic causing Disqus to appear on all pages/posts

When we have ES enabled, Disqus comments appear on all our Wordpress pages/posts, regardless of whether we have commenting enabled (or, more importantly, when we have commenting turned off).

As soon as I disable ES, everything goes back to normal.

Just like your other thread, this isn't an ES problem.

How is it not an ES problem when the problem ONLY occurs when ES is enabled and immediately stops when ES is disabled?

You are enabling/disabling features in WP that is causing something else to change. WP is handling the integration layer here, not ES.