A synonym in this example might be ‘reputation’. He has tarnished/damaged the reputation/legacy of his church/religion...

"Legacy" is often used to mean how someone/something is remembered or effects that are left behind. How an event affects the future or someone's life affects the future even after it's over. For example, if someone created a charity that charity would be the legacy they leave behind. In your example it's a bad legacy -- the negative effects of abuse that people still suffer from even after this person is imprisoned.

So it is work as heritage ,got it thanks