Sorry for the delay, but my work schedule and travel have been awfully heavy lately. It does sound like the issue I'm having is somewhat related to the discussion on https://github.com/raamdev/independent-publisher/issues/155

I've got two separate installs with the same IndieWeb plugins installed. One uses Independent Publisher and the other is a slightly older version of the Academica Theme (v1.2.3 downloadable from https://www.dropbox.com/sh/ym0c78uyzltpeu1/AAByejNd8MG83I2MVOFXOuPaa?dl=0) which is outputting the facebook likes, twitter favorites, and reposts properly (or at least as I would expect.)

For some reason Independent Publisher isn't outputting Brid.gy likes, favorites, or resahares from Twitter and Facebook out of the box the way that Academica (or even WP common themes like Twenty Fourteen or Twenty Fifteen) does. They're not showing up at all. On the site with Academica Theme, I've tried doing a "Live Preview" of the Independent Publisher theme and there, it also seems to be "eating" (not showing) these additional comments from Brid.gy while all the other traditional comments do show up.

However, while you're tracking down the issue(s), you might also consider tweaking one additional output issue with respect to these types of comments. From a UI standpoint for themes using IndieWeb, I would recommend that the comment section sort out the comments and display them somewhat differently. For simple Facebook likes and Twitter favorites, it might be best to aggregate all of them into a facepile [http://indiewebcamp.com/facepile] with a simple header ("Liked on Facebook"/"Favorited on Twitter") followed by the photo icons of the people who liked/favorited the article within those platforms. (This is similar to how most Wordpress sites handle Likes/Stars natively within WordPress.) Following this it could create a facepile of people who reposted/reshared the post. Then after this the rest of the comments should be sorted by date/time as comments traditionally are as this will allow people to more easily read/consume the actual commentary.

This post has an example of a combination of likes/favorites/reposts and actual comments that would be better sorted into a facepile section followed by a more "traditional" comments section. http://boffosocko.com/2015/07/27/algebraic-number-theory-ucla-extension/

I'm supposing that it's how Independent Publisher is rendering the output of wp_commentmeta into its comment section that causes some of these brid.gy-fed likes/favorites/reposts to disappear.

If it helps, I'll also point out a previous and possibly related issue I'd run across vis-a-vis IndieWeb and output of comments: https://github.com/pfefferle/wordpress-webmention-for-comments/issues/1. The solution was most likely the way that the Semantic Linkbacks plugin (an IndieWeb WP-specific plugin) was handling its output. Here it's likely that @dshanske or pfefferle may be of more assistance in sorting things out if necessary.