Michael Coe, 35, saw the two 16-year-olds hugging in the street in Newham, east London, in April and demanded to know if they were Muslims.
Southwark Crown Court heard the Muslim convert then called the girl a "whore", before throwing the boy to the ground.
Coe also attacked a passing teacher who had tried to help the couple.
Judge Michael Gledhill QC said the two children had denied they were Muslim when challenged by Coe.
"Why? Because they were frightened of what you would do if they told you the truth, that they were in fact Muslim," Jude Gledhill said.
He added: "At the time of these offences you either held extremist views or views that were getting very close to extremist views."
Coe had admitted "shoving" the boy - who is half his size - claiming he was acting in self-defence, but was convicted in August of assault occasioning actual bodily harm and battery.
The court heard the father of two was radicalised in prison by al-Qaeda terrorist Dhiren Barot in 2007 while serving an eight-year term for firing a shotgun at police during an arrest.
Coe was also convicted of religiously aggravated harassment in 2013 after seeing a Muslim woman talking to a group of men and telling her that it was against Islam.
The defendant, also known as Mikaeel Ibrahim, became a close associate of convicted hate preacher Choudary, founder of the banned organisation al-Muhajiroun, of which Coe was a member.
Prosecutor Jonathan Polnay read a victim impact statement from the boy.
"He feels the offence has affected his life quite a lot," My Polnay said. "He doesn't see his friends outside of school.
"He has also split up with the girl who was his girlfriend at the time."
An associate of convicted hate preacher Anjem Choudary has been jailed for 28 months for knocking a boy unconscious because he was cuddling a girl.