A lot of the converts of the warrior elite at the time were daimyô in Kyushu or Southwestern Honshu, which is where the trade ships arrived first. Since at the time of the Europeans' arrival the country was not unified, being able to do trade with the bringers of better guns was obviously a strategic advantage, especially if the Christian foreigners brought firearms with them.

So, the simple, materialistic explanation would be - disregarding personal questions of piety in unique cases - that becoming Catholic was seen as a means to improve diplomatic relations with the foreigners, which, in turn, would then facilitate trade.

Oda Nobunaga (the first of the three unifiers, whereas Clavell's novel writes more about the other two) himself, although never converting, also took a cordial stance towards the Christian mission; in his case, apart from economic reasons, that might have been motivated by a desire to curb the influence of the great Buddhist monasteries.

Also, as long as the missionaries themselves did act with prudence and tried to understand the culture they were dealing with in their endeavors, a new religion wasn't necessarily that "alien" as you might think. For the Japanese, virtually all religion (i.e., the many variants of Buddhism) always had come to the archipelago through foreign contact to begin with.

And, as some scholars advocate, even the outlawing of Christianity under Tokugawa Ieyasu (1612) arguably wasn't targeted against the religion per se, but primarily against its permeation of the ruling elite - until 1637, when a rebellion had to be put down which had used Catholic imagery on their flags.