Tomato Shibby has excellent support for the DNSCrypt protocol out of the box. I think it was the first router OS to include it, along with a nice integration in the UI.
Unfortunately, it only supports the DNSCrypt protocol, that Cloudflare doesn’t support. That’s one of the reasons people have been asking if Cloudflare would eventually support this in addition to DoH.
Supporting DoH in Tomato shibby, via an update to dnscrypt-proxy v2, has been discussed on Linksys forums. It is being considered, but hasn’t been done yet; the increase of storage space required to install the new proxy can be an issue on some routers.
So, to recap, it is not compatible with Cloudflare yet.