It's an extremely bold claim. Even if Cloudflare itself isn't a direct threat to people's privacy, the exchange itself still is or can be, so there is no way that the service they provide to people is fully anonymous. Mixers don't even pretend to be fully anonymous, because they know it simply isn't possible because there is a middleman involved.

In case someone initiated a large transaction that requires you to tap into your own reserve at a certain price, what's your policy when the price drops and you are in a disadvantageous position if you proceed with the transaction? Will you just cancel the trade directly or allow some time for the price to recover and cancel afterwards if the price doesn't recover?