A couple of regional leaders at WDW are LDS and I know sometimes the LDS interns under them tend to get Sundays off depending on the department. I'm being vague on purpose because I worked at WDW and I want to someday return.
BYU has an excellent computer animation program, which is a large part of the Disney product line, so yes, Disney and other computer animation companies hire interns and graduates of the program.
With the common (at least in Utah, can't speak for the Mormon diaspora) Mormon fascination/obsession with all things Disney and child-like, it is a match made in, er, Heaven.