Jackie, the key to Michael's "legitimacy" obsession is found in this bit of dialog from GF:
MICHAEL

I'm working for my father now, Kay. He's been sick -- very sick.

KAY

But you're not like him, Michael. I thought you weren't going to become a man like your

father. That's what you told me...

MICHAEL

My father's no different than any other powerful man --

(then, after Kay laughs)

-- Any man who's responsible for other people. Like a senator or a president.

KAY

You know how naive you sound?

MICHAEL

Why?

KAY

Senators and presidents don't have men killed...

MICHAEL

Oh -- who's being naïve, Kay?

To Michael, if senators and presidents can have people killed and can be considered legitimate, then he's no different when he has people killed. If gangsters can own or control casinos in Nevada, where gambling is legal, and can be considered legitimate, why can't he own casinos and be considered legitimate? If legitimate businessmen launder money, why can't he launder money and be considered legitimate? And, if wealthy crooks buy legitimacy from the Church by making massive contributions, why shouldn't he do the same?