"The two others have purple placards hung around their necks: Gender Treachery."

‘Gender Treachery’ is the Republic’s term for homosexuality.

Modern-day Christians are split on the issue. Conservative Christians (like the rulers of the Republic) refer to Leviticus 18:22, interpreting it as a condemnation of gay sex:

Do not lie with a man as one lies with a woman; that is detestable.

Leviticus 18:22 (New International Version)

 Liberal Christians argue that it is a matter of interpretation and translation, and that context is all.  It's worth pointing out that Leviticus also prohibits clipping hair on the side of the head, tattoos, planting two kinds of seed in one field, wearing clothing woven from two kinds of material, and eating shellfish:

Anything living in the water that does not have fins and scales is to be detestable to you.

Leviticus 11:12