If a cable is attached to a support on each side, and there is a load acting on it somewhere along its length.
Is there going to be a vertical reaction force only if the the cable is angled?
Note that the only way to have a horizontal cable is by having the other support higher. But if you do, a horizontal vector will resolve into only a horizontal force. The sin of 0 is zero, so an angle of zero will yield zero vertical force.