Abstract GSOS is a categorical framework for operational semantics, in which rules are modeled as natural transformations of a certain type. Rule systems that fit the constraints imposed by the framework are guaranteed to have desirable properties, mainly that coalgebraic behavioural equivalence, which roughly corresponds to bisimilarity, is a congruence. While bisimilarity is central in process algebra, it is far from the only notion of process equivalence of interest. However, abstract GSOS is not easily applicable to these other equivalences. This work focuses on the other extremum of the linear time-branching time spectrum (bisimilarity being the finest), namely trace equivalence. We wonder under which assumptions on abstract GSOS laws this notion of equivalence is a congruence. A study of trace equivalence for a concrete instance of abstract GSOS (to labelled transition systems with explicit termination) identifies necessary and sufficient conditions to this end. We then transpose abstract GSOS to Kleisli semantics and investigate how, with conditions on the monad (affineness) and the GSOS law (dubbed linearity and smoothness) inspired by the concrete study, trace equivalence can be shown to be a congruence.