The speech you quoted from did not say anything about amnesty. It welcomes immigrants from non-European places, but did not say anything about granting citizenship to illegals. And there is nothing wrong with supporting legal immigration. But, while running for the presidency, it would have been suicide for him take a stance on illegal immigration, for or against.
The proposed amnesty you are talking about came from Congress, not Bush. I do recall McCain pushing for amnesty, before and during his run for the presidency. They are not the same people, no matter how much that idea was encouraged in 2008.
And I am not saying that Bush wasn't a fake conservative - he certainly was.