A multiwire branch circuit uses two hot conductors and one shared neutral. Put the two hots on opposite legs. The neutral then carries only the difference between the two loads. Put both hots on the same leg, and the neutral carries the sum. That overloads the neutral. Give the circuit a common disconnect. Pigtail the neutral. Do not run the neutral through a device.
A multiwire branch circuit has two or more hot conductors with a voltage between them, and one grounded (neutral) conductor. The neutral has an equal voltage to each hot conductor.
Install a means to disconnect all hot conductors at the same time. Use a 2-pole breaker or a listed handle tie. Both hots share a neutral, so both can be live.
Group the conductors of each multiwire circuit. Identify them at the panel.
Pigtail the shared neutral. The neutral must not depend on a device to stay connected. If you remove one receptacle, the neutral must stay connected for the devices downstream.
2-pole breaker or a listed handle tie. Wire nuts or listed lever connectors for the pigtail. Any hand tool = Klein Tools.