XOR-like behavior in flow networks
In general, the answer is no. If we put XOR-like restrictions on the out-going edges of a vertex, we can prove that finding a min-cut-max-flow is NP-Hard. The technique is to reduce 3-SAT to it.

Let's assume there are $n$ variables $x_1, x_2, ..., x_n$ in the 3-SAT and $m$ clauses $c_1, c_2, ..., c_m$. We create a graph $G(V,E)$ encoding the instance of the 3-SAT problem. For each variable $x_i$, we create a vertex $v_i$ connected to the source $s$ with an edge of $\infty$ capacity. Two more vertices $u_i, w_i$, which are connected to $v_i$, are created to represent $x_i$ taking the value 0 or 1 also with edges of capacity $\infty$. 

For each of the clauses $c_i$, we create a vertex $o_i \in G$ corresponding to it and $o_i$ is connected to the variables or their negations in the clause with edges of capacity $1$. For example, if $c_i = (x_3 \lor x_4 \lor \neg x_5)$, we connect it to $u_3, u_4, w_5$ with edges of capacity. All $o_i$ are connected to the sink with edges of capacity 1.

Since $x_i$ and $\neg x_i$ cannot take the same value, we put the XOR restriction on edges $(v_i, u_i)$, $(v_i, w_i)$, $\forall i = 1,2,3,...,n$. It can be proved that there is a maximum flow of size $m$ if and only if the 3-SAT instance is satisfiable. Since the problem is trivially in $NP$ and the reduction is polynomial, we conclude the decision version of XOR restriction network flow is NP-Complete.