First of all, it appears that Arthur Singer's bio of Godfrey contains a fairly notable error. Bal Harbour was not even incorporated until 1946, which is when the Kenilworth-By-The-Sea Hotel was built, so obviously his statement about hotel policy in the 1920s is not true. It may be that Singer confused the Bal Harbour hotel with the Kenilworth Lodge in Sebring, which operated from 1916-2016, but it's about 3 hours from Bal Harbour, in the middle of the state. At any rate, his research appears to be more than a little sloppy. Whether that error impacts the accusations against Godfrey, I don't know. It seems to be very difficult to get a detailed and accurate history of the Kenilworth, and I'm not obsessed enough to keep digging.
But in doing this reading about Bal Harbour, I found this very interesting history of that part of the world (from the Totally Jewish Travel website), re: publicly displayed 'Gentiles Only' signs outside of businesses.
https://www.totallyjewishtravel.com/Kosher_Tours-TL7776-bal_harbour_miami-Vacations.html
Jewish History, POI & Kosher Establishments in Bal Harbour
Until Spain traded Florida to Britain in exchange for Havana in 1763, Florida was subject to the laws of the Spanish Inquisition and Jewish residents were forbidden. When Jews began settling in the area in the 19th century, landlords and business owners routinely posted Gentiles Only signs on their properties. Such discrimination persisted into the 1950s. Today Surfside and Bal Harbour are becoming very popular for Jewish people of all types and practices.
I can't verify irrefutably that Godfrey ended this policy when he bought into the Kenilworth, but I'm reluctant to brand someone a racist or an anti-semite based on rumors, no matter how pervasive. I'll put a lot of value on Dick Cavett's position on this. He is a smart, fair, and honest guy who has a lot of insight into the business.
I do think that history is fascinating.
Edited to add that I would really like to see a photo of the alleged 'No Jews or Dogs' sign in front of the Kenilworth. You'd think that someone would have documented that, especially in front of such a modern and ritzy venue. Per the article above, it seems (unfortunately) that a 'Gentiles Only' sign would just have been part of the landscape at the time. I'm not doubting whether that policy was in place, or making excuses for this dark part of American history.