Speaking to people using the language in which they would describe themselves is as much about politeness as politics. Badges such as this are worn by people wishing to indicate which pronouns are appropriate for them. No-one is born with pronouns. Each of us has an identity that is formed throughout life.
The colours of this badge are the colours of the Trans Flag, which was created by an American trans woman, Monica Helms in 1999. The colours blue and pink are colours that have been traditionally assigned in some parts of the world to things associated with boys and girls respectively. The white it he centre of the flag is to represent those who are transitioning, intersex or who consider themselves as having an identity which isn’t best understood as being either male or female.