If you use TOR cloudflare basically kills your anonymity if you go through it.
But wait there's more.
From around mid September to a few days ago, anything a server that was under their ward had all info put on search engine caches. If you, forsay, had to buy something with your card and the site brooked Cloudflare then whatever you put in the credit card field is available on Google cache.

cloudflare: Cloudflare Reverse Proxies are Dumping Uninitialized Memory
https://bugs.chromium.org/p/project-zero/issues/detail?id=1139

Why cloudflare is cancer to the internet
https://lainchan.org/sec/res/4386.html#4391

List of Sites possibly affected by Cloudflare's, Cloudbleed HTTPS Traffic Leak
https://github.com/pirate/sites-using-cloudflare

Good read.