While very nicely written, I stopped using CloudFlare because of their analytics (which they seem to use in blog posts, and cannot be disabled.) They do watch your site and that is creepy.
Given your feelings regarding analytics, your response (stopping the use of Cloudflare) was entirely reasonable. If you don't want someone to manage your dataflows/cacheing, then you probably shouldn't ask them to.
Your labeling of analytics as "creepy", though, is entirely unreasonable - every hosting company and ISP on the planet that I've ever dealt with, regardless of their politics or privacy position, has always had hyper detailed analytics regarding my sites / racks bandwidth utilization - typically down to 5 minute increments. Furthermore, if I engage them as a provider of Transit and or CDN services, they always have very deep knowledge of who/where I'm sending data to. That's the entire point of why I acquires those services from them - so they can manage them for me.
Any user should be able to opt out of per-site analytics. I don't use Google Analytics or gaug.es or any of that junk because my users deserve better, so tying analytics to your service is a good way to make me not use your service.
Your position is unsupportable. Anonymous analytics is not a threat.
What's next, I can't stand outside and record how many people walk by with t-shirts versus long-sleeve shirts? That's how I see anonymous analytics. Now if you want to argue that the analytics are not anonymous and they can be linked to real people, like that one AOL search-data leak a few years back, then that's a discussion. But you can't say websites/app collecting anonymous analytics is bad anymore than you can say me standing outside in the city collecting visual info on the people walking by is somehow an invasion of privacy. That's just paranoia. You might as well just not use the internet at all if you're that worried because I'm sure whatever ISP you have collects some kind of analytics too. In fact, I'm sure just about every successful business ever has some kind of stats on its users/costumers. You'll just have to exit modern-society if you don't want anyone collecting anonymous analytics from you.
That's a lot different than (e.g.) tracking somebody's click patterns on your site to better serve them advertisements.
And there isn't such a thing as anonymous data in 2013: it's just data that hasn't been identified yet. Surely a small portion of "anonymous" analytic data can be used to match a user's two identities.
How on earth are Cloudflare supposed to do their job if they don't track the users going to your site?
One of the primary reasons to be on Cloudflare is to make use of their security features such as DDOS protection. How are they supposed to tell if you're under attack if they can't monitor the rate of traffic going to your site, or the IP addresses associated with said traffic?
