A better insight would see that opponents of Obama fall into a range of camps, some of which have obvious philosophical and political opposition to his principles and policies, others who are part of a lunatic fringe. It is important to separate out those who use ridiculous hyperbole from those who have genuine concerns. So who does criticise Obama?
Liberal Republicans/libertarians: Obama has had a long political career of advancing more government intervention and spending, support protectionist and spending proposals in Congress and being a generally acknowledged left-wing Democrat. Anyone who believes in less government spending, less barriers to trade, lower taxes and more free market/individualist solutions is likely to oppose Obama. Racist? Anything but. Their rhetoric is likely to fear higher taxes, interference in individual health care plans and the like. However, they have had few friends standing for the White House in a while. I would be in this group obviously, as I believe Obama has some Marxist leanings, a some scepticism about capitalism and individual freedom. A nazi or a communist? No. This SHOULD form the base for opposition to Obama, but is only one part of it.
Mainstream Conservatives: Obama's fairly liberal position on social issues rankles with conservatives, and his belief in a new government health insurer raises some of the same concerns of liberal republicans/libertarians. However, they are also more likely to regard a leftwing Democrat as not being one of them, with different values. They form the Republican base, essentially more willing to believe critics than believe Obama, as they don't trust the Democratic Party. This base, occupied by many religious conservatives, are those who would typically vote Republican.
Hardline fringe conservatives: These are the one who are willing to believe the "birther" rhetoric, fear he is really a Muslim, and believe that he is a communist. This is truly the lunatic fringe wingnuts who are convinced he is willing to hand the USA over to Iran or some other Muslim state, and surrender. They are willing to accept conspiracy theories, and see the great fear as being Obama as a foreign Muslim spy who is "un American" because he is seen to be foreign born. Underlying racism probably contributes to a willingness to believe this. White supremacists, though tiny in number, will encourage this rhetoric.
So it is, naturally, more complicated than Carter says. I've been strongly opposed to Obama, not because of race - indeed his election was a positive sign about the state of racism in the US - but because of his policies. Discussion about his policies and philosophy have long been shrouded by the over enthusiasm for his ability to speak. The content of what he says has been secondary. He campaigned on change, but rarely mentioned what that was, with his own Senate record being one of following almost every leftwing Democrat to vote. None of that showed independent thinking or a willingness to be open minded, rather a basic level of partisanship.
The Obama hype has produced a backlash, from some it is a genuine opposition to a President who believes more government is good, for others it may shroud wider xenophobic and racial suspicions, but I suspect a good part of the opposition represents the dividing line in US politics between the liberal coasts and the conservative centre and south. A dividing line that those who benefit from it seek to emphasise, which exacerbates it. Attacks on George W. Bush and Sarah Palin have long been venal, sometimes I have agreed, but for those who peddle such attacks to claim attacks on Obama are racist is somewhat disingenuous. It is also unwise.
The Republican Party is going through a degree of philosophical discovery at the moment, as it is clear than the evangelical conservative wing is declining in popularity and influence. As that happens, it is the wingnut conservatives that are shouting the loudest, when they are the ones who will permanently deny the Republicans the White House. Republican need to win small government liberals on the coasts to rebuild a wider base. That is the biggest threat to the Democrats. However, branding both the wingnuts and the small government liberals as racist may well be the best thing Democrats can do to bolster Republicans. Many have good reason to be unhappy about Obama. Dismissing them out of hand and insulting them wins no friends.