One of the Issues your Liberals must influence.
In an Arch-Conservative society, homosexuality is illegal and punishable by death. In an Elite Liberal society, gay-lesbian-bisexual-transgendered people are considered perfectly equal to heterosexuals.
Arch-Conservative: Homosexuals are routinely persecuted with no recourse.
Conservative: Homosexuals are not tolerated.
Moderate: Homosexuals are grudingly tolerated, but have few equal rights.
Liberal: Homosexuals have many rights shared by heterosexuals.
Elite Liberal: Homosexuals have equal rights.
How to Influence This Issue
Any method of influencing issues in general has a chance of influencing Gay Rights. There is no way to target it specifically.