In fact, I've found company t-shirts to be a little too "Stepford employee" for my tastes. It's part of a dangerous train of thought where you assume the goals of the company you work for are the same as your goals, or your personal goals must be completely aligned with the company's. Very dangerous thinking for salaried employees, IMO.
On the other hand, sometimes a t-shirt is a t-shirt.
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.
On the other hand, sometimes a t-shirt is a t-shirt.