So which is more humane, allowing people to go free but making them register as sex offenders, or incarcerating them indefinitely on the recommendation of a psychiatrist?
Incarceration, but only if the circumstances require it. Because it does not amount to random public lynching and branding. True, among ex-convicts
any repeat offense is
much more likely than among random people, but a
majority of ex-convicts still does not repeat their crime. The very concept of a "justice state" is that you cannot be convicted of what you have not done yet, and that you should only be punished once. "Offender list" is essentially a lifelong sentence without the chance to parole, without any proof that you would actually do it again. Also, being branded a public enemy does not exactly help one to become a productive, law-abiding member of the society, which should be the goal of any and all punishments, instead of revenge. And, as stated, you get on such a list far too easily even for crimes that do not involve rape, abuse or sex with minors. The severity of the act should have something to do with this, sex with consenting teen half a year under the limit
is different than eg. what 4chan affectionately calls "infant fornicating".
Case in point, here in Finland we do have a well-known individual who first raped, then butchered two little girls. He was declared "insane but responsible for his actions", so even after his prison sentence was finished, he was considered to be a danger to the society and instead of walking free was committed to a mental asylum for criminals. Also, involuntary psychiatric treatment has to be reviewed constantly by independent doctors, so it's not a "recommendation of a psychiatrist". But because of this kind of system instead of a "sex offender list", some drunken fool who just didn't believe "no" but did not beat up or kill anyone, or some fool who harassed his co-eds but since then has grown up, and the like, do not have to carry a lifelong stigma once they have finished their sentences.
However, whether the sentences in
your country (or mine) are too lenient is another thing entirely.