So, then, if a MM were to move to Indiana, for example, he would have to re-work all three degrees to be a MM under the Indiana Grand Lodge...
No, because of the COGMNA that isn't the case as North American Grand Lodges don't require it, but for instance if you go to Europe it depends and most likely will. In theory the Grand Lodge of Indiana could require a Mason from an outside state to re-accomplish the degrees if wanting to join an GLoI lodge, and renounce their membership say in Texas, even though there is full recognition between the two.
if the Mason was from the Grand Orient of the United States and they tried to join Indiana or Texas, then yes they would have to reaccomplish the degrees and renounce their membership, and the GOUSA is 100% white.
So again, it's not so much about race as it is about recognition and masonic tradition. Since GLoTX did not share jurisdiction woth PHA prior to 2006, you would have to do that, as you would with any non-recognized masonic organization. The lack of recognition is racially motivated, the renouncing that you are so hung up can be standard practice regardless of race.
S&F,
-Bro Vick