I have a 69 Firebird. I finally got it 99% done and running after 4 or 5 years of restoring it.
Shifts nice through all the gears when engine not running but will not shift at all while engine is running. Everything is new or rebuilt. I am running a Muncie M20 and a Hurst shifter with a Ram 201 clutch, Ram 401 pressure plate and a Ram 488 throwout bearing. I have had the transmission off and swapped out throwout bearings several times. Most recently was today where out of paranoia and having really nothing to lose at this point, I took everything completely apart to make sure that the clutch disk was facing the right way (it was). Put everything back together and still have the same problems. I am beyond frustrated. Was hoping to drive this car for the first time ever before winter. I am stumped and really need some help.
Thanks in advance..

Are you starting the car in neutral?
I wonder if bellhousing is not aligned to crank centerline. If far enough out of alignment, maybe the pilot bushing is dragging and spinning the main shaft?
Are you sure the clutch is releasing when pedal is depressed?
Don’t know how new all the combination is. Is this something that was all together and ran/drove at one point or all new?
I recall different length throw out fork studs but been too many years ago for me remember what is correct.

Car in neutral. Clutch fork is new, trans is rebuilt, throwout bearing is new, pilot bearing is new, bell housing is stock used but nice, clutch, pressure plate and flywheel are balanced together and came with car new with only break-in time.

Your clutch is not releasing completely. The trans cannot shift when the input shaft is still turning. There is a very small gap between the clutch, disc, and flywheel that is hard to test for. The inspection cover on the bottom of the bell housing is there for that. You remove the cover, have someone press the clutch pedal down, and you test with a feeler gauge for the release gap. To correct this you need to get all the clutch linkage adjusted correctly and it doesn't matter if it is all new or old. When you press down on the clutch pedal, the linkage geometry is designed to make it easy to compress the pressure plate springs. So a foot of pedal travel translates into a fraction of an inch at the pressure plate and disc. Have you adjusted the linkage? The bottom rod is the adjustable part. You want an inch of free play at the top of the pedal, while getting total release at the pressure plate. The clutch fork ball stud is a major adjustment point, and there used to be three different lengths. Now all I see are the tall and short ones, plus an adjustable one. Same with the throwout bearing, there are tall and short ones. A common issue is the clutch fork is hitting the back of the fork opening in the bellhousing, limiting the travel. There are also adjustable spherical ball end upper and lower linkage rods. I am using those because I could not get my geometry correct and they helped a lot. Start at the lower linkage rod. Adjust it so the clutch releases totally. You should not have the pedal hitting the floor, it should be completely released about 3/4 of the way down. Then see if you still have the right free play at the pedal.