Needless to say Catholicism is not at all positive to transgenderism. Transexuals are not allowed to be ordained. An unpublished document forbid the Church from accepting a transgender Catholic's new gender. A Catholic hospital denied breast implants to a transwoman; she sued and the courts decided they must perform the surgery.See Vatican Says Sex Change Operation Does Not Change a Person's Gender. Key to the Vatican's decision is Paul McHugh, the pope's liaison for sexuality. McHugh worked with John Money at John Hopkins working for decades to shut down their SRS clinic.
Read this discussion on intersex and Roman Catholicism.
In many nations, transexuality is equated with homosexuality in the eyes of the law. While transgenderism benefits from having a low profile that governments often don't bother to legislate against us, many do legislate against homosexuality with the death penalty which brings us under indirect persecution. (Iran, India, and Egypt are some notable exceptions from this mistake.) Add to that many transexuals who do not realize they're "really" trans and so identify and act gay. The connection with the Catholic Church is that the UN drafted a resolution calling for the decriminalization of homosexuality (transgenderism not mentioned) but the Vatican officially refused to support it. They said (in nicer words) they would rather allow gays to die than begin the slippery slope that might lead to states being encouraged to legalize same-sex marriage. By extension, this applies to heterosexual transmen and transwomen as well.