Tolkien was definitely not a racist. In addition to being a devout Christian, he was very liberal and outspoken against racism (very much ahead of his time). It is notable that all of his races have aspects of both good and bad; none are truly "greater" than the other. For instance, while the Eldar (elves) are immortal, this is more of a curse - mortality is considered a gift to the men. Elves themselves are not free from corruption, having had ages of strife between them (I.E. the drama involving the Silmarils).
Additionally, while the Dúnedain from Númenor may have had a longer lifespan, or a fairer appearance, than other "races" of men; they are far from a perfect/ideal group of people. Keep in mind that, while most of the Dúnedain were extraordinary men, more than a few of them were just as corrupt as any Orc. After all, they just about destroyed themselves on a dozen occasions.
Speaking of Orcs, it should be mentioned that they are not a race. They are a species. An imaginary one at that (Orcs were wrought by Morgoth, the Dark Lord. They were made to steal, rape, murder, make war, etc.), and any resemblance to a modern day (human) race, if it exists, was purely unintentional. Orcs, and all of Morgoth's minions for that matter, were used by Tolkien to personify all that is wrong, sinful, or harmful to other human beings in the world. They are not European, African, Native American, Asian, or any other race or nationality. They are all of us.
Throughout Tolkien's work, all those carried away by pride, arrogance, or greed eventually fall (Fëanor, Saruman, Sauron, Númenoreans, Orcs...)1. This is a recurring theme that is blatantly evident. And while Gorgonzola's fear that Tolkien was a racist, or used racist themes in his works, is definitely not unsubstantiated, it's highly unlikely.
1 Viggo Mortensen: "As Tolkien said: nothing is evil in the beginning. The potential for evil is in everyone. Evil, like good, is turned to by choice."