The June 18 arson attack followed more than 40 suspected hate crimes committed against churches, mosques and monasteries in Israel and then West Bank and East Jerusalem since 2009, with only a handful of indictments handed down.
In a statement, the Shin Bet identified the two suspects, aged 19 and 20 and wearing kippahs in court, as followers of an "extremist ideology" that believes that "only someone who fights Christianity can call himself a Jew".
No pleas were entered during the court hearing in Nazareth.
The limestone Church of the Multiplication of the Loaves and Fishes, on the northwest shore of the Sea of Galilee, was constructed in the 1980s and is overseen by the Benedictine Order.
It was built on the site of 4th and 5th century churches that commemorated what Christian faithful revere as Jesus's miraculous feeding of 5,000 people with five loaves of bread and two fish.
The fire damaged the church's roof, and a verse from a Hebrew prayer denouncing the worship of "false gods" was spraypainted in red on a wall.
Father Matthias Karl, a German monk from the church, said a souvenir shop, an office for pilgrims and a meeting room were badly damaged, and Bibles and prayer books were destroyed in the fire.
"It's totally destroyed. The fire was very active," he said.
A monk and a church volunteer were hospitalized from smoke inhalation, but the prayer area of the church was unaffected by the fire, he said.
Reuters contributed to this article.