Deaths by Christians
World War I Deaths.
According to World War I casualties (Wikipedia), 10-13 million deaths occured in Christian majority countries of which vast majority were inflicted by other Christians (Russian Empire was largely Christian then).
World War II Deaths.
According to Ryan's answer:
The overall death count estimate of 60 million is reasonable.
The responsibility for deaths in WW2 by country breaks down like this:
If we adopt the stance of the original blog post, where the dominant religion for a country is assumed, we can group the countries and their death counts by religion:
Christians: USA, UK, France, Germany, Italy, Others(for simplicity)
Those countries were responsible for about 20 - 24 million deaths. It
is hard to be precise as it's hard to pin how many deaths in the USSR
were caused by Germans.
Secondary Wars and Atrocities of the Twentieth Century gives us an estimate of around 4 to 5 million.
According to Churchill's Secret War, British scorched earth policy resulted in the death of around 3 million people.
250,000 deaths in Philipine American war.
Vietnam War caused around 1.5-4 million deaths.
4.5 million deaths in Korean_War.
5 million children dead in Iraq due to political sanctions.
The US/ UN sanctions on Iraq of the 1990s, which interdicted chlorine for much of that decade and so made water purification impossible, are estimated to have killed another 500,000 Iraqis, mainly children. (Infants and toddlers die easily from diarrhea caused by gastroenteritis, which causes fatal dehydration). Ref
Deaths by Muslims
After the nationist, secularist and pan-Democratic Young Turks took over the Ottoman empire through the Young Turk Revolution (it was actually a coup), they turned it into a multi party Democracy. Soon these self proclaimed Muslims (who didn't promote any Islamic system nor were religious) launched multiple genocides: (I am saying this because the western press mostly associates these atrocities with Islam or ignores the fact that the perpetrators were secularist pan-Democractic nationalist Turks.)
Greek Genocide - 450,000–750,000
Armenian Genocide - 1.5 million
Assyrian Genocide - 150,000–300,000
List_of_modern_conflicts_in_the_Middle_East gives us an estimate of around 4 million deaths. These wars were largely faught between Muslims.
In the 1960s, a military general took over the government of Indonesia. He violently suppressed communist rebellion by killing around 500,000 - 1 million people. The youth wing of Indonesia's largest Islamist group supported him in that.
Around 200000 Algerians died in the Algerian_Civil_War which is a predominantly Muslim country.
Iran–Iraq War was responsible for the deaths of upto 1 million people.The war was initiated by Iraq's dictator Saddam Hossain who was supported by the United States. US helped Iraq get chemical weapons which increased the death toll. Both parties of the war were Muslim.
139,000–320,000 people died in the Iraqi-Kurdish conflict. One party of the war was supported by the USA and UK.
Subsequently, one month after the Gulf War in February 1991, United States President George H. W. Bush called on the Iraqi people to stage an uprising against Saddam Hussein. This was followed by a series of rebellions in many parts of the country, such as the south by Shi'ite groups such as SCIRI and the Islamic Da'awa Party. Meanwhile, the Kurds in the north staged their own uprising for autonomy, under the leadership of Massoud Barzani, leader of the Kurdistan Democratic Party, and Jalal Talabani, leader of the Patriotic Union of Kurdistan. -- Source
The North Yemen Civil_War resulted in 100,000–200,000 deaths. Its wiki entry says:
On the royalist side Jordan and Saudi Arabia supplied military aid, and Britain gave covert support, while the republicans were supported by Egypt and were supplied warplanes from the Soviet Union. -- Source
In the Bangladesh_Liberation_War, 3,000,000 people died according to Bangladesh's government. It was faught between nationist Pakis vs Nationalist Bengalis.
The article in question seems to have come up with the estimates based on whether the perpetrators were from a group deminated by either Muslims or Christians. Based on the same reasoning, deaths by Muslim dominated groups is around 8-11 million and deaths by Christian dominated one's is around 48.7-58.7 million. (The estimate may need to be improved. I would welcome all suggestions to improve this answer.)
I have entirely removed the deaths due to partition of India because it wasn't due to political violence. No political entities actually supported the violence. It was the result of extreme conditions people faced while travelling huge distances and other reasons.