Can max-flow with mutually exclusive edges be reduced to standard max-flow problem?
You can reduce SAT to this version. Connect the source to nodes $x_1,\ldots,x_n$, one per variable, with infinite capacity. Connect each $x_i$ to two exclusive nodes $x_i^T,x_i^F$, with infinite capacity. Create one node per clause, and connect a literal to a clause (with infinite capacity) if the clause contains the literal. Finally, connect each clause to the sink with unit capacity. The maximum flow is the number of clauses iff the formula is satisfiable.