This quote from Wikipedia: "CNN insiders said that network management had already told Henry that his contract would not be renewed." In short, CNN pulled the plug. Mr. Henry started his journalism career with Jack Anderson, one of the Washington columnists that tended to expose all kinds of nastiness in DC. While not exactly 'right' or 'left', Mr. Anderson claimed to be Mormon. I used to read his stuff in the 1970s, when he was beating the crap out of the Nixon administration, but those were free throws.
People in the media may have a different idea of what is 'ideological' from that of the general public. What mom and pop might consider Left and Right the media simply views as 'markets'. Therefore, Mr. Henry doesn't necessarily have to be conservative, he simply has to appeal to conservatives. This may not take much - don't behave like someone with left wing sympathies.