I'm not sure I understand your post's subtext. Could you clarify what you mean by

for instance how did the fact that many of the leaders of the vanguard of the invasion of Korean impact later assessments?

Firstly, it's important to note that Japanese religions were not unified and there was no 'national' religion at the time that Christianity was first introduced to Japan during the mid 16th century. In fact, during this period of time, there was no nation of Japan even.

This was the period of infamous warfare between feuding warlords called the Sengoku Period, or Warring States Period.

Arguably, the most influential religion at the time was Buddhism, because of their strong military, economic, and political presence. Buddhist sects had armies, large territories from which they collected taxes, and the political connections to influence warlords and nobles.

It's important to note, again, that Buddhism was not unified in Japan. There was (and still is) no central 'church' or authority figure for all of Buddhism. Many differing sects competed and larger sects had internal conflicts and power struggles.

But they were very much like any other major religious organization. They held sway over a great many people, whether common folk, soldiers, or leaders.

So major religious leaders were as much of a political and military player during the Sengoku Period as any warlord.

This no doubt influenced Japanese views on Christianity, seeing it as a new military, economic and political rival. And for religious leaders, a new rival in the spiritual arena as well.

When Christianity first started gaining traction, it was through trade with the Portuguese that missionaries met the Japanese population. This was a significant reason that the Japanese warlords allowed proselytizing in their lands. Portuguese trade meant access to firearms from Europe, which were a game changer on the Japanese battlefield.

Some warlords tolerated Christianity so they could gain access to lucrative and strategic trade with the Portuguese while others were genuinely interested in all the new things these foreigners had to bring to table, whether that was trade and weapons or new ideas and new knowledge.

The common people would have simply seen Christianity as another new religion among many. They were no strangers to competing and differing religions, value systems, and doctrines. Japan had it's own native folk religions, Buddhism, Confucianism, and Chinese folk religions that were all actively practiced throughout the land.

Meanwhile, scholars and other people would have known about Taoism, Hinduism, Jainism, etc. though they were not practiced extensively. But Hinduism did influence Japanese spiritual philosophy because of the connection to India through Buddhism. Another story for another time.

Japanese Buddhism itself had a tremendous number of sects, many often disagreeing with each other over doctrine, interpretation, etc. Japanese native folk religions differed from region to region and often times from village to village. The Japanese spiritual landscape was incredibly diverse and they were by no means united.

That being said, Japanese people might have had their interest piqued at the idea of an omniscient, omnipotent god and singular god. Japanese people would have been used to the idea of a plurality of deities and spirits. Christianity would have rejected this completely, which likely caused conflict philosophically.

But for the common people of Japan, the message of an all loving God that sees all as equal spiritually, whether a lord or a peasant, certainly had appeal for some. And of course, the great many services the Christians provided, like medical care, establishing institutions like hospitals and churches as community centers, would have been welcomed by many.

By the time Christianity had spread and established a sizable community, the Sengoku Period had ended. Now that Japan was nominally united, the new leaders went about consolidating their power. This meant sequestering political rivals, namely the religious organizations that dictated a great deal of policy because of the strength of their armies and purses.

It's during this time that converts are persecuted and heavily ostracized. Christians go into hiding and they establish secret congregations, secret Christian organizations, etc. What's really interesting is that without proper guidance and teachings, many of these groups eventually lost much of their knowledge of mainstream Christian practices and became something entirely different from Christianity.

Many groups changed many of their practices to hide their Christian worship in a desperate attempts to maintain their faith by practicing in form and spirit if not in content, while simultaneously avoiding torture and death. While their devotion was undoubtedly great, it's almost humorously sad that many contemporary Christians would decry them as heretics, that their apparent syncretism was simply a corruption or perversion of true Christianity.

During this time, Christianity is painted as a foreign relic and to be expelled from the country, along with foreigners themselves. Part of the reason is that Japan no longer relied on the foreign trade for firearms, which was certainly a major factor that lead to several leaders adopting Christianity to gain an edge on the battlefield.

Another was that they were seen as a potential threat to the newly formed Shogunate. While we know in hindsight that they would go on to rule relatively peacefully for centuries with few revolts, they could not have known that at the time. They were wary of anything that could tear away their newly obtained place at the top of Japanese society from them. Christianity and missionaries were seen as a foreign foothold in Japan that the Shogunate leaders were not happy to let remain so they took steps to alienate Christianity and Europeans alike.