As far as I know, Christians were hunted, tortured and forced to recant their faith, but there were a small handful of Christian faithful who survived for several generations.
During this time, what was the public opinion of white Christians (Portuguese/Dutch) and of Japanese Christians? Did people support the purge? We're they oblivious to it? How did it change over time, and what happened post-Meiji?
When Francis Xavier first arrived in Japan in 1549, the locals assumed the foreigners were practising a new "Indian faith" because of the ties between the Portuguese and India via their colony in Goa and many of the crew aboard Portuguese ships were Indian converts to Christianity.
For the next roughly 50 years during the Sengoku period (an era of near-constant civil war in Japan) and with the favour of warlord Oda Nobunaga, the Jesuits primarily and other religious orders converted many Japanese -- including several daimyo aka samurai lords, who promoted conversions in their domains. It was hoped that conversions would help stem the influence of the Buddhist monks and foster trade ties with Portugal and Spain, and many daimyo became Christian for potential economic or political gain.
The Jesuits were not passive, but active participants in the politics of the era, often influencing converted daimyo to advance the interests of the church or the Portuguese crown. They had condemned local Buddhist practices as heresy and even encouraged followers to burn Buddhist shrines. There were fears that the missionaries could be the vanguard of a future invasion of Japan by Portugal or Spain, and some of the early missionaries advocated for this to happen. While no invasion plans materialized, the Jesuits often agitated for an increased military presence to protect church interests in Japan. Converts would discard their Japanese names and adopt Portuguese "Christian" names. Over time, this and the Jesuits' aggressive proselytizing created the impression that the missionaries and their converts were foreign agents intent on subverting the social order in Japan.
Under Toyotomi Hideyoshi's rule, these growing suspicions would lead to state suppression of the Catholic faith, persecutions of converts and the executions of missionaries by crucifixion -- the most famous being the Twenty-six Martyrs of Nagasaki in 1597. Nagasaki was the chief port for Portuguese trade and the only port where foreigners were permitted. The Dutch soon became favoured trading partners because they didn't tie their trade to their Protestant religion. The Wars of Religion raged in Europe at the time, and the Dutch allied with the state to drive out Portuguese and Catholic influence from Japan.
Persecutions continued when Tokugawa Ieyasu became shogun with the Battle of Sekigahara and consolidated his power in Japan. The Catholic religion was suppressed, missionaries and converts were expelled or martyred. Many daimyo converts had to renounce their faith to retain their power or go into exile in Macau, the Philippines and other enclaves in southeast Asia. Resistance from some Catholic daimyos and converted peasantry continued sporadically in the early 17th century, as they pushed back against increasing prohibitions on their faith. The shogunate brutally suppressed a large uprising of ronin and mostly Catholic peasants during the Shimabara Rebellion in 1637-38, beheading 37,000 rebels and exiling the Portuguese traders suspected of aiding them.
Catholicism was officially prohibited in Japan throughout the Edo period, but many believers went underground. Authorities would weed out believers and non-believers by compelling townsfolk to trample on a wooden icon of Christ. Those who refused would be arrested. The kakure kirishitan (literally, "hidden Christians") would continue the rituals and practices of their faith in secret. Statues of the Virgin Mary or saints would be disguised as Buddhist deities. Traditions had to be passed down orally, since the authorities could confiscate any printed documents. Without clergy, the community had to rely on lay leaders and over the centuries they drifted away from official teachings.
After the end of the shogunate and Meiji Restoration, freedom of religion was permitted in 1873 and Western missionaries would discover these hidden communities in Kyushu and rural areas.