The men were handed three to six month sentences by the court over the attack, which killed three people.
Christian Solidarity Worldwide (CSW) has voiced concern over continuing violations of religious freedom in Indonesia, the world's largest Muslim-majority nation.
It said the sentences were "astonishingly lenient".
The sentences were passed on the same day as the World Evangelical Alliance’s Religious Liberty Commission warned that the GKI Yasmin Church in Bogor, West Java, could face mass violence if continuing tensions are not addressed.
The church has been forced to hold open air worship on Sundays after it was closed by authorities, violating a Supreme Court ruling permitting the church to operate.
Extremist Islamist mobs have gathered to intimidate and threaten them while the Sunday services are being held.
Earlier this week, the Chairman of the Fellowship of Baptist Churches of Papua, the Rev Socratez Sofyan Yoman, said that churches in West Papua were being threatened by the Indonesian military.
In April, the Regional Military Commander, Major General Erfi Triassunu accused the Church of Papua Gospel of supporting the Free Papua movement.
Churches in the region also say that their churches and homes have been destroyed in military operations carried out in Puncak Jaya since 2004.
At least one pastor is reported to be among the civilians killed.
Rev Socratez said that such “humanitarian crimes” had turned Puncak Jaya into “the most cruel and inhuman place”.
In an "urgent report" issued this week, he called for support from churches worldwide and urged the international community to put pressure on the Indonesian government to bring an end to the violence.
CSW’s Advocacy Director Andrew Johnston is concerned that Indonesia's strong tradition of pluralism, tolerance, and religious freedom was being eroded.
He said that the Indonesian government must take threats to Christians seriously and take "meaningful action" to uphold the rule of law, protect religious minorities, and safeguard human rights.
He also called for a more independent judiciary.
"The shockingly lenient sentences imposed on the perpetrators of some of the worst anti-minority violence in recent years raises serious questions about the integrity of Indonesia’s justice system, and gives the extremists a green light to continue their campaign of hatred," he said.
"It leaves religious minorities throughout Indonesia, not only in West Java, and not only the Ahmadiyya community, vulnerable and defenceless."