I think that there are a couple of elements present in the question. The first is whether or not "tolerance" is a coherent concept. I believe that within the realm of "coherency," there might be some elements present. The idea of being able to accept other people and groups is coherent. Heterogeneous social orders have to be tolerant of those who are different than others. I believe that in this particular notion there might be some level of tension or challenge. At times, this becomes a messy process when one group has limitations towards being tolerant of another. Yet, I don't see this as incoherent. At the same time, I would not say that "tolerance" is limited to one particular group. I think that liberals and conservatives can be tolerant and are tolerant, for the most part. Having said this, if we were to delve into the politically theoretical approach of liberalism and conservatism, I think the classically liberal approach would embrace tolerance more than its alternative because these thinkers, such as Locke or Mill, were driven by the idea that individual freedom and the right to be left alone is vitally important in any political or social order. This becomes where tolerance is most alive.
Tolerance, while often propounded as a liberal concept, rarely truly exists in anyone--conservative or liberal. Liberals who generally stand for social liberty and the right to live as one wants would argue that tolerance should connect more to their agenda than to conservatives'. However, the issue with being truly tolerant is that one has to believe wholeheartedly that someone else has the right to live and think as he so desires. While Liberals claim to support that ideal, when someone who has differing political or sometimes religious views than they do expresses those views, Liberals and others (conservatives and independents included) often engage in namecalling and begin to argue why the opponent should be silent or forced to change his or her views.
The word "tolerance" has taken on a new connotation in recent decades. It denotatively means an indulgence for someone else's view which differs from one's own, but lately, its connotation is that one must virtually take on someone else's views in order to be considered tolerant.