Va. attorney general running against anti-gay Republican
Trump has yet to publicly condemn anti-LGBT crackdown
Hong Kong was chosen over nation's capital and Guadalajara, Mexico
Secretary of State Rex Tillerson urged to condemn measure
Man detained spoke to reporters on Oct. 16
.S. diplomats ordered to leave country after sonic attacks
Heather Nauert wore purple during press briefing
Federal government response has been sharply criticized
Group notes country’s LGBT rights record
Group’s influence declined in recent years