[netflixandkill]

If you participate in facebook etc apps and services at all they have far more insidious and effective tracking and NAT isn't hiding you at all. Additionally the idea that it is granting you any measure of privacy is only true if you're behind a giant translation block with tens of thousands of unrelated people and a broad enough public range that connection correlation becomes impractical, compressing a single family or roommates behind a single public IP that changes maybe every few weeks accomplishes very little if anything.

If you need anonymity that much for whatever purpose, depending on v4 NAT is dangerous at best and you should be looking into anonymous proxies or VPN providers (that also mask ipv6), Onion routing, etc.