There are moments in politics where bonds are forged between ideologically driven base voters and the politicians who take high-profile positions advancing their issues. The base then comes to trust these politicians, and ignores their deviations from the party line or treats them as clever tactical moves. If you were in the GOP base in the Contract With America days when Gingrich led the Republicans to victory in 1994, you probably formed that bond with him. And now you trust him and you're willing to make excuses for him. From the same era, Hillary Clinton had a similar store of goodwill on the Democratic side that made her the presidential frontrunner for a lot of the last Democratic primary. It was a really impressive achievement on the part of Obama and his team to win the nomination over such a powerful candidate.
Now, I'm very willing to believe that Newt's role in the GOP takeover wasn't actually that important, and that his incompetence as speaker made things turn out much worse for the Republicans than if John Boehner could've time-traveled (and seniority-traveled?) into the Speakership of 1995. But I don't think that's what the GOP base voter saw, because Newt was pretty good at getting himself in front of the cameras. The proto-Tea-Partiers have an indelible image of brave Sir Newt leading the charge against big spending and Democratic corruption in Washington, and losing only because of devious Slick Willie and his friends in the liberal media.
Mitt Romney never had such a moment where the GOP base voter really identified with him. Maybe in Massachusetts (I don't know the details here) but definitely not nationally. So people don't have the bonds that lead to making excuses for him. And even if the flip-flopper case were objectively equal against Newt and Romney, GOP base voters would be much more willing to make excuses for their former Speaker than for the former Massachusetts Governor.
(Entirely random personal update: I remember 1994 pretty well myself. I was 14 and a sophomore in high school. I went to the Wake County Democratic Party election night event at a hotel, and the older folks were happy to see a youngster like me there. But obviously it wasn't a very happy place overall. I vividly remember watching the TV announce Chuck Robb's victory over Oliver North in Virginia, as a nice middle-aged black man said "Thank God for small favors.")