This is the Cloudflare resolver, right? What's the "privacy-first" part about? It's just another third party DNS host. They haven't changed the protocol to be uninspectable and AFAIK haven't made any guarantees about logging or whatnot that would enhance privacy vs. using whatever you are now. This just means you're trusting Cloudflare instead of Comcast or Google or whoever.
Cloudflare is making a public pronouncement that they're not going to sell your DNS data nor track your IP address, with the implication that they will also not use the usage data to upsell you services. That's about the only additional "privacy" edge they offer. In the same breath, they insinuate that Google both sells and uses DNS usage from their 8.8.8.8 and 8.8.4.4 resolvers.
Cloudflare is somewhat right: Means, Motive and Opportunity - but for a conviction you have to prove someone acted on the Opportunity. The Motive of Google is tampered with severe risk for loosing trust.
Cloudflare can make an argument they are fundamentally better positioned and that is all they do. As with all US based operations the NSA may cook up some convincing counterarguments and we may never know.