How should the thermostat wires be connected to my furnace?
Move the green wire to the outdoor unit from the G terminal to the B/C terminal.

In the wiring diagram for your outdoor unit, the green wire from that unit is connected to the blue wire going into the outdoor unit wiring, which connects to the C terminal on the "comfort alert" (compressor monitor) module.  Connecting that green wire to the G terminal connects the circuitry in the "comfort alert" module in series with the input circuit for the control board's G terminal, which means that the current that powers the module is flowing into the G terminal, turning the input on and causing the control board to run the fan all the time.

The fix is easy: moving the green wire to the outdoor unit to the B/C terminal on the control board causes that current to flow back to the other side of the transformer instead of taking a detour through the G terminal input circuit, and will restore the normal blower functionality of your system.