What caused the original split of the Mame32 team?
History:
Mame started as a DOS program. Mame32 came up as the windows devivative. Mame32 had two web sites, the "official" one and the "QA" one. (Mame was a 32 bit DOS program, but ignore that for a second.) Mame switched for DOS to command-line windows around (IIRC) 0.36b15 - 0.36b16, done basically by Aaron Giles. Mame32 had to make some changes to work with the new changes, and it took a couple b# releases for them to do it. The person in charge of the "official mame32" web site at first didn't release source code with the binary, then released part of the changes, and the rest as compiled .DLL files. Neither fit with mame's license.
Others behind mame32 decided to release the source, but from the "QA" site. The "QA" site became, and still is, the official mame32 site.
As to
why some didn't want to release all the source is just guesses, IMO.
And why is the Christopher Kimse/Michael Soderstrom version considered illeagle?
Back then, those versions went against Mame's license because it didn't release the whole source code (nor all the differences from the official version). Now with the current source, not releasing the source isn't against the new license
as long as "mame" is not part of the name. However, they'd still go against mame's current license if they released as they did and called it "mame32".