Gnosticism (from the Greek gnosis meaning knowledge) is a general idea that divides the world into the Spirit which is good and the Body which is evil. The early Church had gnostic groups which believed Jesus' death symbolized death to both Sin and Body and that the Creator God of Genesis was in fact the devil because he imprisoned all people into body but God the Father sets us free from the flesh. Gnosticism includes some other, important beliefs too, not entirely relevant to our discussion here. This is heretical to orthodox Christianity because we believe that God created a "good" physical world and our spirits and bodies are two parts which together make us us. The Nicene and Apostles Creeds both renounce Gnosticism by stating, "We believe in the resurrection of the body."
Most objections to transgenderism are twisted or misinformed, but this objection, while not entirely accurate, is not without some accuracy and can serve as a warning. In the trans community, we hear a lot of language that only the mind/spirit matters, not our body. However, while this could be called semi-gnosticism I don't think a gnostic would care for transgenderism at all for a number of reasons.
First, a transexual believes that their spirit is either male or female. A gnostic believes that male and female are bodily and temporary divisions. The spirit which is eternal is neuter, neither male nor female. Consider the Gospel of Thomas, a prime example of gnostic belief that says a person can only enter the Kingdom of Heaven by making the female like the male and the male like the female. I.e., becoming androgynous.
Second, the goal of a transexual is not gnostic. A gnostic encourages dis-identification with the body. While a transexuals does that partly in denying their birth sex, they also desire a body of the correct sex to enjoy and express themselves. A gnostic would not desire any kind of body because the body is the prison. It is incapable of expressing the spirit, at least not well, and bodily/"fleshly" pleasures are sinful.
For transexuals to be accused of gnosticism is not only incorrect it is hypocritical. One moment they are accused of ignoring and hating their bodies the next they are accused of loving it too much. The latter is shown by criticism of transexuals for spending too much time on their bodies through makeup, hormones, SRS and so on. They are also accused of fetishism which they delegate as a physical and not a spiritual pleasure. Many critics are less interested in assigning correct analysis as they are assigning blame.
If transgenderism were to be accurately accused of gnosticism, it should be the genderqueers who deserve it! Some genderqueer people (not including myself) believe they are not either female or male. They tend not to have surgery but may take low dosages of hormones to give them a more gender neutral appearance. Even these people can easily hold their gender identity without being gnostic. If they simply value aspects of their body other than their sex - eating, playing, moving, singing, touching, feeling, etc - they are embracing their body. They might believe that the Resurrected Body is sexless and that sex is a temporary phase of the body (like an umbilical cord or breathing water) that we eventually grow out of and they are merely mature for their age.
Allegedly, "[T]he Church of England’s 2003 discussion document also equated transsexualism with the ancient heresy of Gnosticism." See Some Issues in Human Sexuality – A Guide to the Debate, discussion document from the House of Bishops’ Group on Issues in Human Sexuality, Church House, 2003, page 249.