There appears to have been a change on the Twitter end of the connection so embedding Twitter feeds in the Widget Connector no longer works. When embedding a Twitter URL and clicking preview nothing is displayed, even though the instances had their whitelists disabled.
This behaviour has been reproduced in Confluence v4.3.7, v5.1.3 and also on the EAC. When changing the embedded URL for a YouTube video the content was embedded as expected, which suggests this is Twitter specific.
Related WC ticket: https://ecosystem.atlassian.net/browse/WC-61