An employer can't dictate who your "real" friends are, or who your Facebook "friends" are (if this your personal Facebook account and not your company's account) without stomping all over your constitutional rights, including freedom of speech and association.
Your employer can lawfully tell you not to use Facebook during business hours, and they can proscribe limits on accepting gifts from frineds/clients, but they absolutely cannot tell you who you can socialize with and associate with on your own time and in ways you choose. If your employer persists in making insane rules that are supposedly for your "protection," the ACLU might be interested in getting involved on your behalf.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.