"You will perish," the unidentified man shouted outside the Bristol home of Christian Martin. "You will be destroyed," the man tells him.
He chants: "Same sex relationships are wrong, bestiality is wrong, homosexuality is wrong, same sex relationships are wrong, sexual immortality is wrong, bestiality is wrong.
"Come to the cross before it's too late. Jesus loves you but he doesn't love your sin. However if you reject Jesus Christ and what he did for you at the cross you will perish. If you reject Jesus Christ and what he did for you at the cross you will be destroyed."
The man says "everything in the city of London will collapse and this country will be brought to ruin unless it turns back to Jesus Christ before it's too late."
In the video, the politician can be heard to say "ok thanks very much, thanks very much, it's very early in the morning could you stop please". But the man continues chanting.
He said: "I fly a rainbow flag outside my house to celebrate Bristol's diversity and my sexuality, had so many compliments and thumbs up so never had a problem with it, until today."
His neighbours have since approached him and offered to fly the LGBT pride flag in support of him.
Avon and Somerset police confirmed it was investigating a hate crime incident.
A spokesman told Premier: "A man, carrying a large wooden cross, was filmed shouting abuse towards a house displaying a rainbow flag. Officers have spoken to the occupant of the house to offer support and reassurance.
"We're now looking into whether the occurrence is connected with any other similar incidents which have recently been reported to us."
Officers urged anyone who has been subjected to hate crime to report it.
"We will always support anyone who is victimised and work closely with all communities to stamp out crimes motivated by prejudice and hate," said Inspector Tim Hill.