Fisherman: Criminals go to lawyers because they commit crimes.
People go to lawyers when they are charged with a crime. No criminal goes to a lawyer because they committed a crime. They go because they're being charged with one.
Fisherman: But a lawyer disclosing privileged information
If a client admits to committing a crime, that is not privileged information and it is not a crime to report that to the police. The lawyer may choose to treat it that way, if they prefer to serve their client at the expense of victims and of society at large.
Similarly, a clergyman who reports a crime to the police (especially something as heinous as child abuse) would not face sanction for 'violating' privacy or confidentiality. In other words, they're not forced to withhold this information-- they choose to. The government isn't protecting criminals. The government is protecting religious organizations. Religious organizations are protecting criminals.