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?