Equivalence between MIN UNCUT and MIN-CSP_XOR
Suppose we are given a set of constraints of the form $b_i \oplus b_j = c$. We construct a graph with one vertex corresponding to each $b_i$. For each constraint of the form $b_i \oplus b_j = 1$, we add an edge $\{i,j\}$. For each constraint of the form $b_i \oplus b_j = 0$, we add a new vertex $x$, and two edges $\{i,x\},\{j,x\}$.

We can think of a cut as a partition of the vertices into two parts. For a constraint of the form $b_i \oplus b_j = 1$, the constraint is unsatisfied iff $i,j$ belong to the same part iff $\{i,j\}$ is uncut. For a constraint of the form $b_i \oplus b_j = 0$, there are two cases:


If the constraint is unsatisfied, then $i,j$ belong to different parts, and so exactly one of the edges $\{i,x\},\{j,x\}$ is uncut.
If the constraint is not unsatisfied, then $i,j$ belong to the same part, and so (depending on the location of $x$) either zero or two of the edges $\{i,x\},\{j,x\}$ are uncut. Since we are aiming to minimize the number of uncut edges, we can assume that zero are uncut.


In total, the number of unsatisfied constraints is the same as the number of uncut edges.