Many people that share political/religious items do not care if they are false. They agree with the premise of the item, the facts are just a nuisance. Please will always think something is false if they disagree with it and accept as fact anything they agree with. This goes across all ideologies and can be seen rampantly everywhere.
When I first got on the internet, early 90s Usenet, I thought this is great and will dispel all of the nut cases with crazy ideas and conspiracy theories. Most Usenet groups that I visited had some very smart people who were quick to point out fact when superstitious idea came up. In a very short period of time groups started to pop up that offered every crazy idea known to man and the major participants were the people with crazy ideas. Now the internet offers a support system for any crazy thing you want to believe. Even if everyone around you in real life tried to convince you it is a crazy idea, there's a support system waiting for you on the internet.
What makes it even worse is the impersonal nature of on-line communication. People will say all kinds of stuff on social sites and email they would never say in person. This is making us less civilized. When you live in a community and interface with your neighbors you learn to live with and accept the views of others. Even if you don't believe the same way or maybe think they are crazy you learn through life to live and let live. Now with the internet you have the choice to be a fanatic about anything and only interface with people with the exact same outlook as yourself.