Were the British colonists who opposed the revolution being pragmatic or were they anti-liberty?

I think this question threatens to overstate and oversimplify the motivations of the Loyalists. They comprised a wide range of experiences and perspectives, comprising perhaps as much as 1/5 of the colonial population. When describing their mindsets, we have to expect something fractal, because as we look into different regions and communities or differing occupations, we should expect the context and the details to change. It's a general feature of history that people tend to be complicated, and the same goes for events, ideologies, political movements, and about any field of study you can think of. The closer and more comprehensively we look, the more these easy generalities begin to break down.
So, as to the question itself, are the loyalists driven by pragmatism, or anti-liberty? I would certainly admit that there were those driven by pragmatism. For one thing, there was every reason to expect the British to win the Revolutionary War, and therefore it would have been quite reasonable, on the grounds of self interest alone, to side with the British rather than run the risk of being branded a traitor. To this, we can also add those whose personal interest was tied directly with Britain — if you have a governmental post, for example. Financial and economic self interest would apply here as well. So, as to the first half of your question, I think pragmatism has to be recognized as a feature of the Loyalist Cause. It tends to be a very common human motivation.
Beyond that, I tend to question your use of the label "anti-liberty." Personally, I think this choice can be better phrased, because the word "liberty" has significant and wide reaching implications, and is actually a key theme in Eighteenth Century discourse, one that is often paired and contrasted with that of tyranny. Indeed, you see this particular theme featuring heavily in the Revolutionary Period, and even within Britain itself. To say that the Loyalists were anti-liberty... I think that's unfair and overly simplistic to the Loyalist cause, because for many Loyalists, the Revolution would have been seen as an act of armed rebellion against a legitimate governing authority. It's a long running theme of Colonial History that the Colonists saw themselves as British subjects. In fact, even during the lead up to the American Revolution, the Colonials still perceived themselves as British: this is where the argument of "No taxation without representation" came from — the claim here was that they had been denied the legal rights they were owed as British subjects. A key theme of the Revolution is that, at some point, there was a break, a transformation within the Revolutionaries themselves, where they stopped viewing themselves as loyal Englishmen, and began to see Britain itself as a hostile force. The Loyalists would not have experienced that break. With this in mind, I find myself doubtful that many, if any, of them would have been "anti-liberty" at all; "anti-independence" perhaps, but liberty is a bigger and more far reaching term. I think it would be more accurate to say that, for the Loyalists, Britain would have remained a legitimate governing authority, and that the Revolution itself had crossed a line by raising arms against it.

Those American colonists who supported the British had a variety of motives, some more honorable than others. Many genuinely believed that it was a bad idea for America to go it alone and declare independence from the mother country. They thought it was crazy for Americans to turn their back on a long-standing arrangement which, despite its various ups and downs, was still on the whole beneficial for the colonies. Independence was presented by Loyalists as a leap in the dark that would almost certainly lead to war against what at that time was one of the most powerful militaries in the world. The ensuing bloodshed, chaos, and disruption that would ensue simply wouldn't be worth it.
So pragmatic considerations certainly played a part in opposition to the revolution. Some Loyalists may well have been sympathetic to certain of the patriots' grievances, but they thought that staging a revolution over them was an exaggerated response. Far better, they thought, to sit down with the British and try to reach a peaceful, amicable solution.
It would probably be overstating the point to say that American opponents of the revolution were hostile to liberty in any way. Americans of all persuasions were strongly committed to the ancient liberties which they believed were their birthright. It's just that Loyalists tended to believe that the existing arrangements, though far from perfect, were tried and trusted, and thus provided a much better means of protecting liberty than a completely new system built from scratch.