Omar has accused Greene of using political ads to target Omar for political violence.
He said Chan's mental health issues led to "misguided attention seeking" and "provocative engagement with others."
The 39-year-old YouTube star has been denied bond and will be held until a hearing on September 16.
Greene County Sheriff's Office have also warned that "this is an ongoing investigation with additional charges pending."
Only three U.S. states allow sexual contact between consenting adult relatives.
Chris Chan, otherwise known as Mrs. Christine W. Chandler Sonichu, is a webcomic creator, artist, blogger and YouTuber.
"If we had known about the relationship between [Hertha's mother and father] we would of course not have recommended the two polar bears for breeding. That was a mistake."
The man was also found guilty of repeatedly raping one of the children he fathered with his daughter.
Senator Tom Cotton, an Arkansas Republican, repeatedly blamed "unelected justices" of the U.S. Supreme Court for establishing abortion rights that he said should be set by legislatures.
Dr. Yashica Robinson said she was "appalled" that rapists could receive a lesser punishment than she would for completing an abortion.
House Minority Leader Kevin McCarthy said Thursday he opposes Alabama's abortion law because it doesn't include exceptions for rape, incest and the life of the mother, which he falsely claimed are part of the Republican platform.
Steven Pladl is thought to have shot his daughter-wife and their son.
Jammey Willenbrink's wife, Brenda Willenbrink, was also charged with two counts of felony complicity.
Skeletons of four, unrelated men offer major insight into the sex lives of our early ancestors.
The judge ordered the release of a man sentenced to 10 years for having sex with his cousin.
How can the fantasy drama's incestuous relationship get any darker?