Is a jet engine's shaft neutral in the direction of thrust?
Thrust is produced in the compressor; as its blades push the air backwards to compress it, a reaction force pushes the blades forwards. These blades are fixed to the shaft. The shaft has a flange on it which pushes against a similar face on the engine mounting, in an arrangement known as a thrust bearing. This in turn transmits the thrust to the airframe.
A turbofan has extra big blades which push more air backwards, adding to the thrust.
The turbine blades draw work from the exhaust flow which slows it down, so they push against the main thrust and in a simple single-spool design can even require the thrust bearing to face backwards.
Heating the compressed air in between is what makes the thing work at all. Also, the acceleration of air out the back of the combustion chamber creates a thrust reaction against its forward wall. For a pure turbojet, and especially for a centrifugal compressor, this will be greater than the compressor thrust. It might not be as much as one might suppose because the chamber is relatively small.
For supersonic flight, the air intake acts as a shock compressor to generate most of the thrust, while the exhaust nozzle can be made to generate more by expanding high-pressure exhaust against a divergent nozzle. At high enough speeds the spinning bits just get in the way.