To give everyone an idea of what we're dealing with in Acadian records, here are some baptism records from Diocese of Baton Rouge Acadian Records 1707-1749... the records that were carried in exile. They say at the beginning on p. I-4 that "The spelling of surnames varies widely in the registers. Spellings used by the priest have been used in the abstracts even where they differ from signatures." I could have used the "actual" records that are available on familysearch and Canadiana but those are actually transcriptions/ copies made in 1895 and not the originals themselves. So this seemed the closest way.
Here are 5 baptism records for the family of Jean Breau and Anne Gautrot.
*Anne Bro (Jean Bro and Anne Gautrot) bn. 18 Feb. 1733, bt. 18 Feb. 1733 spo. Charle Heber (s) and Anne Grange (SGA-2, 123)
*Charle Braux (Jean Braux and [omitted] Gotrot) bn. 18 Oct. 1727, bt. 18 Oct. 1727 spo. Charle Grangé and Marie Flan (SGA-2, 79)
*Francoise Breaux (Jean Breaux and Anne Gautreau) bn. 18 April 1723, bt. 18 April 1723 spo. Charles Gautreau, grandfather, and Marguerite Landry (SGA-2, 38)
*Jean Pierre Breau (Jean Breau and Anne Gautrot) bn. 24 Dec. 1724, bt. 24 Dec. 1724 spo. Pierre Gautrot and Margueritte Hebert (SGA-2, 56)
*Joseph Brau (Jean Brau and Anne Gotrau) bn. 27 March 1726 bt. 27 March 1726 spo. Jean Dousette (s) and Marguerite Gotrau (SGA-2, 67)
So this one family would have children with different surnames: Bro, Braux, Breau, Breaux, and Brau. That hardly seems reasonable There is no one spelling more common that the other and there is no one correct spelling.
The Acadian project via an open discussion on G2G discussed how and when to standardize and nobody at the time disagreed! Most posters were grateful for the standardizing. The discussion was held in the Policy and Style forum and all steps as mandated by Wikitree in their directions as to proposals. Here is the original proposal... but there were lots of threads at the time about issues with name spelling and this addressed them. https://www.wikitree.com/g2g/16598/standardizing-early-acadian-names