Yes, they can. Having to register as a sex offender severely restricts one's ability to live a normal life. Many States pile on unnecessary restrictions, like prohibiting access to social media websites. Recently, in Packingington v. North Carolina, the Supreme Court ruled that limiting access to social media websites that we all use evert day, such as Facebook, Twitter and LinkedIn, impermissibly restricts lawful speech, in violation of the First Amendment. So if the Judge or your probation officer tell you that, as a sex offender, you're not allowed to access social media, they are wrong.