I see this distinction mentioned from time to time and it doesn't make sense to me. IMO, your actions not being tracable to your identity is privacy. In this framing, anonymity is part of privacy. You desire anonymity because of the privacy it gives you. Which is not to say that anonymity is always required for privacy though it tends to strengthen it.
Similarly, sometimes people say there's a tradeoff between security and privacy, which doesn't make sense since privacy (confidentiality) is one dimension of information security.
If you still disagree, could you attempt at defining privacy and anonymity and how you can prioritize meaningful anonymity without caring about privacy?
There are two sense of "privacy". Actual privacy, which of course is subsumed under anonymity, and the fake "privacy" that everyone is telling you they have a policy about and are assuring, while they track you and collect personal information.
Food for thought: Rather than nitpick on people who apparently use the word in earnest in its actual meaning and thereby conceding that those policies are actually "taking your privacy seriously", rendering the word void of meaning, we educate and take it back?
Saying "Make sure that it's impossible for my online actions to be traced to my identity, and then I don't need privacy" is in a way giving up on privacy alltogether.
Probably a push back against the commercialization of the term privacy to now mean "we get your data and share it widely for money making purposes, but here are the terms so you have privacy."
"Privacy policy" is definitely one of the most prominent Newspeak terms around today. The full term should read "how we'll violate your privacy policy".
Similarly, sometimes people say there's a tradeoff between security and privacy, which doesn't make sense since privacy (confidentiality) is one dimension of information security.
If you still disagree, could you attempt at defining privacy and anonymity and how you can prioritize meaningful anonymity without caring about privacy?