Answer
Pansexuality and omnisexuality are closely related. Pansexuality is sexual attraction to people with no recognition of gender. Omnisexuality is sexual attraction to people with recognition of gender. Practically speaking, there is no difference between the two. Both pansexuals and omnisexuals are sexually attracted to heterosexual men and women, homosexual men and women, bisexual men and women, transgendered men and women, gender-fluid men and women, etc., etc. The difference is that a pansexual claims to not see gender at all while an omnisexual sees gender but doesn’t care. The unofficial slogan of both seems to be “hearts not parts.”
The Bible does not specifically mention pansexuality or omnisexuality. But, since pansexuality and omnisexuality sometimes involve sex with the same gender, the biblical condemnations of homosexuality would apply equally to those who practice pansexuality or omnisexuality (Leviticus 18:22; 20:13; Romans 1:26–27; 1 Corinthians 6:9). The only form of sexual activity the Bible supports is heterosexuality within the confines of marriage (Acts 15:20; 1 Corinthians 6:13; Galatians 5:19; Ephesians 5:3; Colossians 3:5).
The recent trend to ignore gender or even deny it entirely is absolutely unbiblical. God created man and woman and designed them to complement each other, not just physically and sexually but also emotionally and spiritually (Genesis 2). To deny male-female distinctions and embrace alternative forms of sexuality, such as pansexuality and omnisexuality, is to deny reality and, more importantly, to reject God as Creator and Designer. Simply put, to engage in pansexuality or omnisexuality is sin.