Thank you for explaining the Haiku a lot. I got it!
I believe the thoughts of Zhu Shunshui has a great influence on Japan at that time. Information shows that Mitsukuni even honored Zhu Shunshui as his own teacher which is really a very win-win cooperation! After all, Ming Dynasty had been defeated and replaced by Qing Dynasty, but Zhu Shunshui, being a stubborn Confucian scholar refused to submit himself to Qing Dynasty, still being loyal to the old Ming Dynasty and at last he was forced to leave China like a homeless person. We can imagine how grateful he would be when he was respected and treated so well by Mitsukuni in Japan.
I guess it is because Confucianism emphasizes on loyalty, Buddhism doesn't, so Mitsukuni didn't like Buddhism. But maybe I am wrong since it is only my opinion.