Guantanamo Bay Camp X-Ray (as opposed to the naval base that has been in US hands for over a century) is a secret prison. The outside world and independent organizations such as the UN or the Red Cross do not have access to the prisoners on a regular basis. In this way, it is an extralegal prison, one run outside of the norms of international law. My point is that, as pohnpei states, we don't know everything that goes on there and probably never will.
But as racism exists everywhere in the world to varying degrees, we can assume that it exists in this prison as well, and we can guess that it exists to a greater degree than in other places because it is run by a military that is at war with al-Qaeda, and a military that has taken losses of personnel and perhaps even family members against al-Qaeda, so the degree of dislike and even hatred may be higher than it is among the general population in other places. All we can do is guess, though.
There really is no way to answer this question with any degree of actual knowledge. After all, none of us (presumably) has spent any time working as a guard at Guantanamo and therefore we cannot know what the true feelings of the guards are towards the detainees.
There is surely some amount of animosity on the part of the guards towards the prisoners (just as ex-students of mine who have served in Iraq and Afghanistan have expressed negative attitudes towards the natives of those countries). But it would be very hard to determine whether these attitudes are based on racism.
When you have people who are presumably anti-American, it is not surprising that Americans (and especially members of the US military) would express animosity towards those people. But would that animosity be based on race? That is much harder to say. The animosity could just as well be based on religion or simply on the fact that these are people who (we are told) were involved in trying to attack Americans.
So, there is surely ill-will towards the detainees, but it would be hard to prove that the ill-will is based on race.