It's a facepalm for a lot of reasons that I can see:
1. The sex offender registry is a joke, including everyone convicted of everything ranging from streaking, peeing in public, and teenage lovers having consensual sex to sexual assault and violent rape. The idea that it serves any utility in filtering out bad people is laughable - the vast majority of people on it are completely harmless.
2. When you type a name in, there's simply no guarantee that any names you find in the registry are actually the person in question, particularly for common names like "John Smith". You'd have an exceptionally high false positive rate.
3. It's trivially easy for someone with malintent to circumvent this check. All it takes is a fake name & ID.
4. This assumes that all sex offenders have records, which is just false. It does nothing to stop any bad guy who hasn't yet been tried and convicted of a crime.
Further, the blogger is just wrong on at least one point. A nudist club is a private facility and the management is perfectly within their rights to reject someone because of a "gut feeling". As they're not places of public accomodation, they're not subject to anti-discrimination laws.
And finally, the blogger also seems to be promoting a police state and witchhunt mentality among nudist clubs, which I'd take exception with. While this policy wouldn't do anything to stop a determined ne'erdowell, it would certainly annoy someone like me enough to keep me from going.