Manual transmission stuck in reverse in my mx-5 miata even though shifter appears to be in neutral position

Sounds like the clutch needs bled.

Your shifter may have come loose and slipped out of position. This video may help.

https://www.youtube.com/watch?v=hMGU_3CCUBg

http://www.techguys.ca/howto/transmission_fluid.html

In addition to this site I have heard that you can remove the shifter boot and plate for easier access to the fill hole.

Sounds like a problem with the cable or shifter. look at the front of the transmission where the cable conects. Have someone move the shifter through its positions and see that the cable is moving the transmission lever properly.

The one item I would suspect is the through-out-bearing not completely disengaging the pressure plate from the fly wheel. If the vehicle is in neutral and you slowly depress the clutch and release it do hear a singing or whining sound? Since you cannot adjust the clutch any more the through-out-bearing is the component which moves the pressure plate from the fly wheel to stop the power from the engine to the transmission. It is difficult to shift when the engine is on because the fly wheel is still engaged and powering your transmission.

Yes you most likely have a bad throw out bearing. If you replace the bearing you would do yourself a favor and replace the clutch and pressure plate while you are there.

check the gear stick make sure it did not come out of place

sounds like shifter fork inside transmission has broken, literally snapped in two.

Unscrew shifter Knob.

The lower shifter boot is attached to the transmission by 3 10mm bolts. You will need to remove to center consoule and the upper shift boot that attaches to the car to be able to remove the lower boot. Then you can replace the lower boot.