What is the sexist part? That two men have a fight to marry a female airplane engineer/mechanic? That a woman runs a restaurant and is holding out for some man?
Said women repeatedly calls out that behavior. The pointlessness and harm caused by macho culture is a theme throughout the movie.
If you think it's objectifying and sexist, that's a you problem.
Even as a child in 1960 I watched women fix aircraft, lifting out engines and stripping them.