I wouldn't want to wear the t-shirt of the company I work for (even though I like said company), because it feels too "rah-rah-rah, we're so great!" to me. But I love to wear t-shirts of vendors and platforms that are awesome (GitHub, for example, or Twilio, if I used Twilio.)
And man, I would never wear a LinkedIn t-shirt. Pinnacle of lame (no offense, LinkedIn people, your product is very useful! But not cool.)
Yes, a LinkedIn shirt would be lame, because everyone uses that service, and (in my perception) people who talk about leveraging synergy were on it before geeks were. So it's neither a cool group nor an exclusive one. Whereas a Github t-shirt says, to other coders, "I am a coder who works with open source." And to non-coders, it means nothing.
Coolness is mostly about exclusion, I think. Or to put it more nicely, it's about identifying with people you like.
So if a coder can honestly say "I think Brand X is awesome, and those whom I want to impress also think that," he/she might wear a Brand X shirt to a conference. Otherwise, no.
And man, I would never wear a LinkedIn t-shirt. Pinnacle of lame (no offense, LinkedIn people, your product is very useful! But not cool.)