The Professional Footballers Association (PFA) chairman said players are entitled to take a stance over racism.
As one of the bodies which funds Kick It Out, the PFA also defended Rio Ferdinand in the face of possible sanctions from United boss Sir Alex Ferguson.
Ferguson said Ferdinand's decision not to wear the t-shirt was "embarrassing" and promised to "deal with it".
PFA chairman Clarke Carlisle told BBC Radio 5 Live: "We will definitely monitor the [United] situation very closely and make sure Rio Ferdinand's rights as a human being, never mind as a footballer, are not undermined in this position.
"Everyone has a right to free speech - just like you can't coerce anyone into shaking hands, you can't make somebody wear a T-shirt - although I do personally believe that joining in with the campaign is the best way forward.
"And then for all these players to get together and put what it is they want down on paper so we together as a union - all the players, one with another - can make those changes and move forward."