Contact information is redacted by default. I've moved a bunch of domains over, they're all redacted in the whois without me taking any action. It lists the registrar as Cloudflare. It shows the domain updated date, the creation date and registry expiration date. There are no contact details listed at all. And it shows the DNS servers (in this case the Cloudflare LOU and MAY name servers).

In fact the sole problem I've had, is with another registrar. I've had my domains with GoDaddy for 15 or 17 years. I've never had a problem with them, so it was fine, but they've begun seriously pushing their prices up (now about double what Cloudflare is charging). All the transfers from GoDaddy to Cloudflare went super smooth, took minutes, except for one high-value domain I've owned since the 1990s. GoDaddy is quasi attempting to hold that hostage, they put it through some kind of manual transfer intervention that will take a week to complete (hopefully).