Tinfoil or tin hats is a term that originated from people wearing tinfoil hats to keep out the "alien signals" and is generally used to describe the super paranoid or conspiracy freaks.
A fan is said to be wearing a "tin hat" or engaging in "tinhattery" when they are convinced they are being sent secret signs that their boys are really IN LOVE and DOING IT, for example secret messages being sent through the clothing that Jared and Jensen wear. Blind items in gossip columns are also a common source of secret information.
Any information that appears to contradict this belief is rejected and said to be the work of the Network PR mavens or other evil doers (such as fake girlfriends). Weddings to people of the opposite sex are claimed to be merely elaborate means of concealing the true love, in this case of Jared and Jensen. Conspiracy theories abound.
The adherence to their beliefs by tinhatters often manifests in extreme obsession with the topic, as well as being vitriolic towards anyone challenging these beliefs. This may include direct attacks on people associated with Jared and Jensen through Twitter or blogs. To observe some extreme tinhats in their natural habitat you can visit the anonymous community spn_gossip
These people are a very small minority in fandom.
The majority of fans happily consume and produce fanfic and fanart based on the idea of a relationship between actors, and approach the fantasy in a playful way. These fans may make comments in reaction to a photo of Jared and Jensen together along the lines of "oh they are so in love", but this is connected to the fictional constructs of the actors, and the fan is aware it is not fact. These fans may use phrases such as I am putting on my tin hat to indicate that the author realizes the fiction of what they are saying but are happily indulging in their RPS fantasies.
Admittedly distinguishing fiction and reality can be hard for even the most rational fan when co-stars start sharing a house.
An annual activity at the fan convention WinchesterCon has been the Tin Hat Parade, which involves fans making real tin hats out of aluminum foil.