So how is it the company can “refuse to let them quit” or “force” an employee to go to a temple? What is the actual enforcement mechanism other than guilt?
Japanese companies have some culture of bullying and harassment. The laws against it are limited and enforcement is toothless. But yeah, it's mostly ultimately a lack of courage from the employees in question.
It’s definitely illegal, labor rights are pretty strong in Japan. I think your typical Japanese person is just very compliant when faced with an uncomfortable situation and bad bosses abuse that dynamic.
Labor rights are far stronger in Japan than countries like the US, but like regulations everywhere, are only as strong as they are actively enforced, where companies suffer meaningful penalties for violating them. Japan is by no means a place where this is true, such that companies fear violating them.