Below is a list of books I have found helpful on homosexuality and transgenderism from a Christian perspective. Each book has its own page with an overview, quotes, and a link to Amazon.
Speaking of Homosexuality: Discussing the Issues with Kindness and Clarity, by Joe Dallas. Dallas identifies five different types of supporters of the LGBTQ+ movement. He includes helpful rules for engaging in these conversations and plays out the debate on common questions.
God and the Transgender Debate: What Does the Bible Actually Say about Gender Identity? By Andrew T. Walker. Walker raises and addresses several questions about gender dysphoria. He also gives helpful teaching on a biblical response to those struggling with these issues.
Affirming God’s Image: Addressing the Transgender Question with Science and Scripture, by J. Alan Branch. Branch gets into the details of the scientific arguments around transgenderism. He also digs into the difference between “someone who experiences gender dysphoria and someone who embraces a transgender identity.”
Embodied: Transgender Identities, the Church, and What the Bible Has to Say, by Preston M. Sprinkle. Sprinkle begins by looking at the definition of biological sex and then what is meant by gender identity. He then spends time walking through all the permutations of these gender identities and offers some practical ways we can empathize with those having these experiences.
Two Views on Homosexuality, the Bible, and the Church, by William Loader, Megan K. DeFranza, Wesley Hill, Stephen R. Holmes, Stanley N. Gundry, edited by Preston Sprinkle. This is an academic book written by biblical scholars. The contributors touch on many liberal theories of biblical exegesis that will confusing and off-putting to a lay evangelical audience. If you are dealing with arguments about homosexuality at an academic or denominational level, this book is a good resource.
I will add other helpful books to this list as I am able.