So what you say is true, there is definitely many local rulers, tribes, and lords who willingly converted to christianity, the most revered and notable of whom would include leaders like Constantine of Rome (byzantines later), Clovis : king of the franks, Reccared I: King of the Visigoths,Edwin of Northumbria, Vladimir I of Kiev, Olof Skotkonung, and so on and so forth. I also made an error saying that the missionaries were backed by the military, although the missions would occasionally ask the local militia to find natives that ran from the spanish missions (The natives were essentially slaves to the missionaries).
The natives were 'slaves' to the missionaries? Really? The natives worked on the missions in the same way that monks worked in a monastery - given that they were, by norm, treated far better by the missionaries than actual slaves on plantations, including being given a pretty solid education, and the missionaries more often than not protected them from slavers and were the biggest voices for native rights in Europe, it can hardly be said they were treated, as a whole, like slaves. There are even rare examples of older missions being run by native clergy themselves.
Heck, one of the charges leveled by the Marquis of Pombal was that the missionaries were hindering the Portuguese government's exploitation of the natives (of course, he didn't put it that bluntly, but with how the natives were treated after the Jesuits were expelled it's plain to see that was one of his motives).
However, the issue is that these conversions took place primarily from the 4th - 10th century and then we only see 2 or 3 notable conversions from the 11th -15th century.
And this proves your point, how? All it proves is that earlier missions were effective at converting the natives - as the amount of unconverted natives declines, naturally so will the amount of notable conversions.
There were also numerous steppe tribes who converted to Christianity or Islam during the 11th - 15th centuries, and they most certainly were not forced.
EU4 takes place at the second half of the 15th century - 1812 and at this point we have enter what is called the "Colonial era" for Christianization, where willing conversion was virtually always performed as a ceremony in order to reflect respect on behalf of the natives of North America, South America, Africa, and the East Indies towards their new neighboors - the west (Spain, Portugal, England, Dutch for the most part). These were conversions motivated by fear, fear created by the genocide of, subjugation of, and enslavement of native populations.
More rubbish. Let's start with the East Indies, shall we? As mentioned in a post above, European powers actively discouraged missionaries since it meant they would have to treat the natives on more equal terms - there was not a single nation in Indonesia who converted to Christianity, and barely any of the tribes (most of who converted were in the Philippines, and converted willingly to get assistance from Spain against rival tribes ). Islam, however, did gain quite a following in Indonesia, due to the willing conversion of the ruling class. Africa never experienced any widespread or even notable colonization during this period beyond South Africa, and very few Christian missionaries or missions (Islamic on the other hand...), and the Kingdom of Kongo converted before the Portuguese had established a notable presence in the region.
North and South America were the only places that actually saw widespread missions out of that list. In South America, the missions functioned mainly in protecting the natives from the Colonists, and providing some sense of civilization. In North America, if someone wanted to set up a mission, they had to ask permission from the tribe itself - sometimes if they declined, it ended with the missionary dead. In addition to the added benefit of protecting said tribe from the colonists, if the missionaries mistreated the natives they could - and did when it actually occurred, which was rare - simply rise up and destroy the mission.
Furthermore, the centuries might have changed but the motives remained the same; common reason for conversion was better relations with nearby powers, Christian or Muslim, along with the hopes of protection, better trade, and better technology. Given that there are numerous incidents of natives converting when the European powers weren't even close, it shows that there was certainly a lack of fear of them, if not an outright fear of their coreligionists that caused them to seek alliances with foreign powers - not something uncommon. Or, perhaps even more difficult for the modern mind to comprehend, perhaps there were even conversions that were undertaken simply because someone
wanted to convert, and benignly at that.
For the Most part these horrible acts were committed by England, Spain, and Portugal, such as encomiendas (the granting of forced native labor for Spanish colonists), and Portugal officially and unofficially "trading" for slaves in the Kongo and Ndongo.
Ah, here it is; the European 'atrocities', I was wondering when this trope would come into play. Yes kids, remember; it's a worse crime to destroy local traditions and bring basic human rights and civilization to other people than let widespread practices of cannibalism, human sacrifice, ritual mutilation, pederasty and other atrocities that would most certainly be denounced today if the Europeans hadn't nearly wiped them off the face of the earth continue.
The encomienda system was not perfect, but it was not slavery. It was a dependency system similar to feudalism that started and caught root in Spain itself, and then was used in the colonization of the New World to help meet labor needs and build up infrastructure - and it was still conducted in a way very similar to feudalism, even incorporating native leaders into it as being held responsible for organizing the people under them. It crossed the line into slavery when the colonist assigned to oversee a group was overzealous in production, but given that the Spanish Crown had banned slavery of the natives and passed multiple and extensive laws in regards to the native's rights as early as the 1540s (championed primarily, of course, by missionaries), the natives could simply appeal to their local audiencia, which were tasked with ensuring the royal laws regarding natives were enforced.
Heck, sometimes the encomienda system simply replaced a local native system of the same kind, such as the Inca's mita system (except the encomienda was notably less brutal).
As for the African slave trade - it was an indigenous system that existed long before any of the Colonial powers set foot on Africa. It was old enough that early Islamic caliphates tapped quite heavily into it, and it continued as it always had when Portugal decided to enter it.
And funny that you would bring up England and provide absolutely no examples of their crimes.
The point is that during the time period in which EU4 takes place it would not make sense to allow natives to willingly convert unless they are bordering and are threatened by a Christian power, or receive an event that goes along the lines of "the signs tell us we should embrace Christianity" after bordering a Christian nation. I am not sure that it should be allowed for pagans to convert to other religions, such as Islam, since the sources I read mentioned the Muslims being particularly unconcerned for the most part as to the religious beliefs of those they bordered, except when it came to Christians.
Then I'm just going to take a wild guess and say your sources are biased against Christianity (which would not exactly be uncommon) in how they tout supposed atrocities by the missions, completely ignore the natives own habits or the spread of Islam, and simply sum up every conversion during this period as 'we need to convert or we'll die!!1!'.
But there's only one meaning of the word pagan, and that is everyone who is not Christian.
Pagan - "a person holding religious beliefs other than those of the main world religions."
Just because the word first emerged in Christianity doesn't mean other religions didn't adopt it or already have their own words for it.
Nevertheless, the missionaries did convict people of the fact that Christianity was right, even though many of the Asian princes and kings did not adopt Christianity themselves.
Sorin Otomo, Ujisato Gamo, Ukon Takayama, Joan Naito, Kanbei Kuroda, Harunobu Arima, Sumitada Omura, Yukinaga Konishi, Hidekane Kobayakawa, Nobukatsu Oda, Nobuhira Tsugaru, and so on and so on.
Granted, Japan has always proven itself to be a... special case in many things.