What an absolute twerp.
Previously infected have been getting the virus again, and in some cases have been hospitalized and have died of reinfections: https://ehrn.org/articles/covid-19-testing-and-possible-reinfections
Serological data from Wuhan shows that at 12 months, about 20% of previously infected have become seronegative as their antibody levels wane. Antibodies declined on average by about 70% from their initial levels at the 12 month mark: https://www.biorxiv.org/content/10.1101/2021.04.05.437224v1
Neutralizing antibody levels have been a correlate for protection from symptomatic Covid: https://www.nature.com/articles/s41591-021-01377-8
A number of the new variants have escape mutations that evade prior infection immunity including P.1, B.1.351, and B.1.617.2: https://www.cdc.gov/coronavirus/2019-ncov/variants/variant-info.html
To date we have seen no variants that evade the vaccines.
Rand Paul had his positive test in March 2020. There's a significant chance he's seronegative at this point. At the time he said he was asymptomatic. Asymptomatics are more likely to not generate high antibody responses from infection, more likely to see their antibody level decline earlier, and more likely to go seronegative in the first months than symptomatics: https://www.nature.com/articles/s41591-020-0965-6
More centrally here he's framing the matter incorrectly. You don't just get vaccinated to protect yourself. His prior infection may possibly protect him from severe disease and death, but at this point even if that were true, he's much more likely to be infected again and transmit the virus than if he were vaccinated. He should get vaccinated if not for himself for vulnerable persons around him. He's a practicing opthalmologist, so he's a high risk for contact with the virus and putting his vulnerable patients at risk unnecessarily. And he's putting his vulnerable Congressional colleagues at undue risk.
What an asshat.