I have had two conversations each with intelligent liberals and conservatives, and a whole lotta FB sharing and blogreading added in this week. Small sample size, but I think I notice something.
When something is reported in liberal media and conservatives read it, their response is "this is one-sided...this leaves out important facts...this is trading on what things can be made to look like, not what is actually so..." and then degenerates into the usual rants that partisans engage in.
When something is reported in conservative media and is read by liberals - and this seems to be entirely in the context of an item reported by a liberal site quoting a conservative site in limited context - the response is "this isn't true...this didn't happen...I can't believe how ridiculous/bigoted this is that anyone would even believe this..." At best, there is the suggestion that this is a one-off event, which conservatives are putting an enormous amount of emphasis on. Then there is no rant, just dismissal, down the memory hole.
If even mostly, rather than invariably true, this would still be a profound difference.
For the record, this is on the following currently-fashionable topics: Syrian refugees (there are no others, it seems), the unraveling of Obamacare, and campus racism.