NP-completeness and reduction of MAX-XOR-SAT and MAX-2-XOR-SAT
MAX-2-XOR-SAT is a generalization of the more familiar problem MAX-CUT.

To see this, consider a graph $G=(V,E)$. We will have a variable $x_v$ for each $v \in V$, and a constraint $x_u \oplus x_v$ for each edge $(u,v) \in E$. We can identify a cut $S \subseteq V$ with a truth assignment by $S = \{ v \in V : x_v = 1 \}$. You can then check that the number of clauses satisfied is exactly the same as the number of edges cut by $S$.