The men were convicted of online harassment and threats of violence, their prison sentences ranging from four months suspended to ten months' jail time.
The Paris criminal court acquitted a fifth man in the case.
Barbara Butch -- her stage name -- was inundated by hateful messages after the Olympics opening ceremony in July last year.
The body-positive feminist was at the centre of a scene including dancers and drag queens during the show that was reminiscent of depictions of the Last Supper, the final meal that Jesus is said to have shared with his apostles.
Organisers said they intended to portray a pagan feast and meant no offence, but religious and far-right circles, including Catholic groups, French bishops and US President Donald Trump -- a candidate at the time -- slammed the scene as being a disrespectful parody.
During a hearing in September, Barbara Butch said she had "just wanted to bury herself and disappear at that moment". She said she developed agoraphobia and psoriasis after the harassment and needed antidepressants.
Her lawyer, Audrey Msellati, said the threats had severely impacted her client's health, causing insomnia, months of nightmares, weight gain and fear of leaving her home.
The defendants present at the hearing, including a student, a father and carer, admitted to sending messages but denied they were threatening or constituted harassment. Several said they were offended by what they saw as a "parody of religion".
Only one defendant, who was not present, was sentenced to a prison term that must be served behind bars due to "extremely serious acts", the presiding judge said in the decision.
Other artists involved in the Olympics opening ceremony were also cyberbullied, including chief choreographer Thomas Jolly.
Seven people were found guilty in May for bullying him online, receiving fines and suspended sentences.