Simple solution: Charge people for using Homebrew who don't want to send analytics in, fund Homebrew development with those funds. Otherwise, its an external cost being foisted on the volunteers by developers who want privacy at the cost of additional volunteer time.
EDIT: The tone of this thread is the exact problem with open source projects and participation. "I want a say, but I'm not willing to contribute in any way except use your tool you're providing for free." Sad, but expected.
There are many OS projects out there with larger needs than an analytics server that have managed to get the support they need. If resources are an ongoing problem you even have the option of applying to join a free software foundation like Apache that has resources.
There's a reciprocal arrangement here. One of the requirements of joining the Apache Software Foundation is using "Apache" when refering to the name of the software product for the first time in a new context, e.g. first mention on a webpage. Apache Groovy was promoted from Apache's incubator last November (2015), so I've been doing just that ever since. Unfortunately, many of the developers who work on Groovy don't bother, availing themselves of those resources but not giving back to the foundation the small amount asked.
Alternatively, fork it, take out the modifications, and run your own version of Homebrew. But that takes time, and effort; that same time and effort homebrew devs are trying to save with a feature. Why is your time as a user valuable but the Homebrew dev's time not?
They could have a prompt with a countdown, you opt in it you don't say 'no' after a minute.