Someone with nothing better to do than to spy on their neighbours for signs of petty wrongdoing. A derogatory term for members of the neighbourhood watch and other such organisations.
The term refers to the only sign of their presence - curtains twitching in suburban dwellings as they peek out at whatever might be going on outside.
Has absolutely nothing to do with homosexuality, except where homosexuality is illegal and thus something else for the curtain-twitchers to report to the authorities.
"Letting the deranged curtain twitcher at Snout’s Cottage gather “intelligence” about her neighbours reminds me of East Germany before the Wall came down."