His parents seem supportive of his relationship with her and they kinda perfectly balance one another out. She's super lax and carefree, though to the point of negligence at times, and he's responsible and hyper-fixated, though this can lead him to be overly guilty.
They're kinda like the yin-yang of one another and make up for one another's weaknesses, which is something I think ideal relationships should strive for.
I say give 'em a few years and his parents will let 'em get married.