Could Cloudfare be preventing realclimatescience.com as a scam? It's name looks too similar to realclimate.org, which is an award-winning climate website. If you are selling a sweetened soda, you cannot call it Coca-Cola-Drink.
https://www.cloudflare.com/ does display, even on Firefox 45, which seems odd. Why would they display their own website, but not that of a paying customer?
Cloudfare's web page says they protect against threats, and a websites with a fake names are a legitimate threat. Not that the realclimatescience.com website is a threat. It's just an opinion website. Everyone is entitled to an opinion. The name of the website does seem a bit questionable.
Incidentally, realclimate.org does not display on Dooble or on Firefox45. Cloudfare does not seem to be involved.