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Feel like it depends on your tolerance for mud a bit and the actual shape of the tyre on the rim. There are pics on the internet of people wedging 1.9 and I'm sure I saw some 2.1s in somehow.
I also intend to try this this winter. But I have a sense that maybe the actual answer if you want a CDF with 650b tyres is a Fugio.
https://www.bikeradar.com/features/genesis-croix-de-fer-853-br-builds/ this is a modern CDF frame clearing 47s, just about.
I'm currently thinking of selling my hardtail due to using my CDF more and more for all off-road duties. Would be using proceeds to get a 650 wheel set and some chunkier tyres than my current 700x40, so would be interested to hear your ongoing reports!
what tyres are they in the photo?