2005 rx8 clutch wont disengage

It sounds like something not put back correctly or adjusted. Was the slave cylinder arm push in when you bled the system? There may be air behind it. Did you use a pressure bleed system, slave up to Master. Lots of help in the links.

https://www.google.com/search?q=2005+6+hyundai+tucson+clutch+master+cylinder+replacement

https://www.google.com/search?q=2005+6+hyundai+tucson+clutch+adjustment

When I do clutch jobs. I replace the clutch package(comes with the slave) and the master cylinder also. Have the flywheel turned or replaced. Just a note. The clutch plate can be installed backwards. No matter how many times you bleed it, It won't work.

Check clutch fluid level in clutch master cylinder for proper level. You can also watch the slave cylinder move at the transmission where it pushes on the clutch fork. The slave cylinder should move when the clutch pedal is depressed. If the cylinder does not move, suspect a defective master cylinder/slave cylinder/air in system that will require bleeding. If all moves, suspect tranny removal for inspection

`Did it bleed, did fluid come out in a steady stream? Isn't there a spring to bring the pedal off the floor?
Check the linkage of the pedal to rod to the clutch master cylinder, make sure that is all together. Any chance the master has an internal leak and won't build hydraulic pressure down at the slave? If you get it bled, then watch the slave operation while someone works the clutch pedal. The piston on the slave should extend and push the clutch fork enough to disengage the clutch.

so if the the slave cyl. moves to max and the clutch does not disengage, then the throw out bearing is destroyed, ,first it burns up, seizes or collapse to a shell of nothingness.
the hyd. clutch is self adjusting, so there is no calibration like on cable or rod systems...
if its bled right the slave moves full distance.
so.... T/O bearing is GONE , end of the road.

No ---it simply needs the air being bled out of the clutch system. IF the slave cylinder had no fluid leakage past the piston then have an assistant help you bleed the slave cylinder. If there is a problem then I would consider replacing the clutch master cylinder .Keep an eye on the clutch master cylinder reservoir . The play you gave in the clutch fork is not there when the system is bled properly and there is no spring as the system keeps the piston of the slave cylinder in contact with the forks.

Check the hydraulic clutch operation. This is a clutch master cylinder with a reservoir on the firewall, and a clutch slave cylinder down on the bell housing of the transmission, with a steel tube running from the master to the slave cylinder. When clutch pedal is depressed, hydraulic fluid (brake fluid) is forced from the master to the slave. The slave cylinder should push out a little plunger that contacts the clutch fork lever-pushing it forward to engage the clutch.
Add brake fluid to the reservoir if needed. Watch the plunger on the slave cylinder: if it moves little, or not enough, try bleeding the slave from the bleeder valve. They are bled just like brakes. If bleeding doesn't help, your clutch master or the slave may need replacing. The master cylinder, like a brake master, has internal seals that hold hydraulic pressure, so force can be applied to the plunger on the slave cylinder.

can you see leaking hydraulic fluid anywhere? The principle is very simple The master cylinder behaves like a syringe. You press the clutch pedal and fluid is forced by the master cylinder plunger to the slave cylinder mounted on the side of the gear box. The slave cylinder is like a syringe in reverse so that the fluid pushed into it from the master cylinder causes the plunger to extend into the clutch/flywheel bell housing and engage with the end of the clutch bearing release lever. The slave cylinder has a bleed screw on the top of it to release any air that has got into the system. Ensure that reservoir is full and ensure that a sheet of polythene has not been left under the screwed on cap: sometimes done to prevent excessive fluid loss whilst working on hydraulic systems. Make sure that the hydraulic unions at the master and slave cylinders are nice and tight. make sure all bled points are similarly tight. The only possible remaining places for air ingress (and by default fluid egress) are the cylinder fluid seals on the pistons... get under and look for leaks when you can get a colleague to pump the clutch repeatedly

TO Bearing is Bad and Trans WILL Be Intermitten With Proper Operation one time and Improper Another, Also Check Flywheel Thickness Against Specs

I have often found that the very action of bleeding the clutch causes the slave piston to move forward drawing any air away from the bleed nipple.
Try pushing the piston all the way to the back of the cylinder and holding it there in some way and if you can detach the slave from the gearbox, allow it to hang by the hydraulic pipe and this in it self will cause any air to rise to the rear part of the slave and hopefully out through the bleed nipple.
Because I did this job regularly on MG Midgets which gave you a 6" by 2" access hole at the bottom of the drivers side footwell to carryout this operation I eventually made up a tool from a piece of flat bar and a long bolt, I used the mounting holes of the slave and two nuts and bolts to hold the flat bar and the long bolt via a welded nut on the flat bar to push the piston back.
I feel your pain.