If I had to guess the meaning of transphobia independent of context, I would guess it means “fear of crossing.” Sample sentence: “Hiram was unable to cross the street after the light changed due to his transphobia.” After reading about it in the context of an article at the Daily Mail, I understand the term to have considerably less meaning and considerably more baggage. The article explains:
Children as young as three are being asked to sign a contract pledging not to use transphobic language at school.
The pledge is contained in a ‘home-school agreement’ which all children must sign before they start at Turnham Primary School in September.
Read more at LibertyUnyielding