How many times over that period was the Red Sea either mud or sand? I’d say more than a few.
Since these dates are “between 125,000 and 43,000 years ago”, just once or twice.
https://www.cdm.org/mammothdiscovery/wheniceages.html
[snip] There were at least 17 cycles between glacial and interglacial periods. The glacial periods lasted longer than the interglacial periods. The last glacial period began about 100,000 years ago and lasted until 25,000 years ago. Today we are in a warm interglacial period. [/snip]