Murderers don't tend to be uh, murder aficionados, as it were. They usually want to kill a specific person for a specific reason and once that is done they are done. It
may indicate a certain lack of self-control that could be dangerous to be around, but there is a lot of study of this. People convicted of murder and later released have relatively low recidivism rates (eg committing any crime), and very very rarely ever commit another murder.
People who commit sex crimes, more than most other categories of transgression, tend to do it multiple or many times, and they follow certain patterns of escalation. Someone who has committed a sex crime is fairly likely to do it again, or do similar or worse things.
I'm not arguing in favor of life-long registries or retributive justice at all. But the practical experience with different categories of crimes don't always match our intuition about what sorts of people are dangerous, and that may warrant treating different crimes differently after the fact as well.
And then mostly unrelatedly, the "sex offender registry for urinating" thing is largely a myth you hear on the internet. The registry is public so you can and should go check it for your area just to get an idea. You may need to look up some unfamiliar legal terms, for example in my state there is no charge of "rape" only "aggravated sexual battery." Around me and in most places I've lived, the vast majority are for unambiguous violent sexual crimes, or crimes against minors under age 13. Simple exposure and "it was a month before her 18th birthday" are what you hear about on the internet but are actually quite rare.