Gruden out It depends on the extent of it. There have been NBA players (Kobe I remember specifically) who have been fined for using homophobic language. A white WR was fined years ago for using the n-word out of anger at a concert. A similar thing would probably happen today, though maybe they'd be suspended for a game, which seems fair.
The difference is twofold. One is the extent to how often Gruden used these types of language. I'm not naive enough to believe the incidents Kobe and the WR were fined for were the first time they used that language. But you can't punish someone for a hypothetical. But this wasn't one incident from Gruden. It was a series of emails showing that this wasn't a mistake out of anger. This is who he is. The other guys could theoretically argue it was a one time thing (though again, I wouldn't believe them). Gruden can't. Secondly, Gruden is in a position of power, which means you're held to a higher standard. And for a league that has issues with a lack of diversity among its coaching staffs, having a racist coach who only hires white OC's and DC's is a problem.
So to answer your first question, if it came out tomorrow that Tom Brady did the exact same thing as Jon Gruden did, I would hope the Bucs would cut him instantly and would be disappointed if they didn't.
As for your terminology of "being fired for life", I'm not sure exactly what that means. Should Gruden ever get a job in the NFL again? No, he shouldn't. There are plenty of coaches out there who could do just as good a job as Gruden without being a bigot. He's made millions of dollars in his life and won't suffer one bit for it. The league is better off without him.
College coaches and administrators should too. Hell, if it came out that one of my bosses at work did the same thing as Gruden, I'd expect him to get canned too. The obvious difference is it would be easier for my boss to move on and get a different job than Gruden, but my boss also isn't a multi millionaire.
Racism is bad. Homophobia is bad. Sexism is bad. These aren't mistakes you are. It's who you are as a person. And there are consequences for being a bad person.