What term is used for a person whose gender identity conflicts with his or her birth sex?

The term "transgender" refers specifically to individuals whose gender identity does not align with the sex they were assigned at birth. This encompasses a diverse range of identities, including those who may transition to live as a different gender through social, legal, or medical means. Understanding transgender identities is crucial in the context of diversity and inclusion, as it highlights the variety of human experiences regarding gender.

Other terms provided in the question describe different concepts. A cross-dresser typically refers to someone who wears clothing traditionally associated with a different gender, often as a form of expression, without necessarily identifying as that gender. Celibate refers to someone who abstains from sexual activity for personal, religious, or other reasons, and does not relate to gender identity. Lastly, lesbian refers specifically to women who are attracted to other women, which is a sexual orientation and not tied to gender identity. Thus, the accurate term for someone whose gender identity conflicts with their birth sex is indeed "transgender."