According to the Roman Catholic Church, an inverted cross is commonly referred to as the Cross of St. Peter. As of 2014, this same symbol has been co-opted by popular culture in movies and television shows as an anti-Catholic symbol.
The Cross of St. Peter is a representation of humility in the Catholic tradition because upon his execution the Apostle Peter is said to have requested his crucifixion be performed upside-down. It is believed that he felt he was not worthy to suffer the same execution as Christ. As of 2014, the Cross of St. Peter is a symbol commonly associated with the Papacy, as the Pope is believed to be Peter's spiritual successor on earth.
Other common symbols associated with both the Pope and St. Peter are the Keys of Heaven. This is because, according to the Bible, Peter was to be the cornerstone of Christ's Church and was gifted with the keys to the Kingdom of Heaven.
It is also not uncommon for inverted religious symbols to be used as a representation of a faith's antithesis or opposition. This may be why movies which delve into stories of demonic possession or satanic acts so often utilize these symbols to represent the influence of their antagonists.