I think it should be registered but only accessible to law enforcement for judicial purposes.
The label 'love offender' is a very, very broad term that encompass many crimes. You can get 'aggravated child sodomy' on the registry for receiving a lewinsky from your girlfriend or something iirc. problem is, nobody who reads that charge in a job interview wants to hear the explanation behind it.
i wish people were more educated about this stuff. when someone hears the word 'love offender' they automatically assume they're a child rapist which in most cases is very very inaccurate.