As Digby points out, Newt Gingrich's sudden desire to play the good cop is driven almost entirely by his personal political calculations. Newt's rise to power consisted largely of being in the right place when white Southerners stopped voting for Democrats for all federal elections, not just the President, and demagoguing things like midnight basketball and welfare reform (in fairness, Newt had plenty of targets, the most famous of which is somehow blaming liberal Democrats for Susan Smith killing her children). He has made some effort to get black Republicans elected, but as you can tell from the Republican caucus, it hasn't had much effect.
But if you are a Republican and wanted to win elections without changing your platform, Newt's your man. The easiest way to do maintain the party's policy status quo would be to win the Presidential nomination and then say to the country "I'm not as racist as those mean ol' Democrats say I am" and then maybe put together a 2000-era Bush tax cut where you have mammoth tax cuts for the rich, "but I'll get my $300". If you can find a few African-American Republicans and give them prominent roles in your campaign and convention it might work. For the Republican donor class and conservative apparatchiks who are still heavily invested in Bushism, that's a much more palatable path to victory the embracing a Grand New Party/Christian Democrat approach or a Teddy Roosevelt-esque small-but-effective tack. Fear Newtism, for it is perhaps the only way Republicans can end up in power while still leaving in place the ideas and people who have wrecked the country over the last decade-plus.