Complex sentence: Lesbian, gay, bisexual, and transgender (LGBT) people and their allies have a long history of campaigning for what is generally called LGBT rights, also called gay rights and gay and lesbian rights.
Split into simpler sentences: Lesbian, gay, bisexual, and transgender (LGBT) social movements share inter-related goals of social acceptance of sexual and gender minorities. LGBT people and their allies have a long history of campaigning for what is generally called LGBT rights, also called gay rights and gay and lesbian rights.