Theoretical CSPs where (in)equality constraints can be expressed as a single constraint?
In complexity theory, CSPs are usually specified as a set of allowed predicates. If the (finite) domain is $D$, a predicate of arity $d$ is an arbitrary subset of $D^d$ of allowed values. In particular, equality (or inequality) is a predicate of arity 2.

This is the point of view taken in Schaefer's dichotomy theorem as well as the more recent universal algebra approach (see for example a short survey by Libor Barto). Another example is the celebrated Raghavendra's theorem, which states that assuming the unique games conjecture, every CSP can be approximated optimally using semidefinite programming.