To make cabinet doors that meet my level of satisfaction requires a lot of work. The trade off is I never have failures. Most would scoff but, here goes.
I purchase material 15/16" hit and miss planed. Cross cut 1" over length for stiles. Rip thru a straight line saw 2 1/2" wide. Depending on board width and style length it might get ripped twice to insure it's as straight as it can be. I joint one face and plane to .82 thickness. This insures the part is not twisted. Using an out board fence on the shaper I run stick (Freeborn Tooling) Rails are coped before sticking. If there is any tear out or grain fuzzing I can re-run the part changing the width. The outboard fence allows for part width and making it as straight as can be. It also allows for shorter rails to be run thru with the power feeder. It's as perfect as I can make. I re-cut the parts to 60mm wide. This cuts off any tear out the cope cutter left. You could set the out board fence on the shaper to cut final dimension. I chose not to.
After door assembly there is still 3mm to trim off all the way around the door to get to final size. I build an european cabinet and expect my doors to be exact. I never have out of square doors, wrong size nor ones that are twisted.
As for your four wheeled feeder, mine has a gap in the center so I set two wheels in board and two wheels out board. If your cutters are new or have been sharpened (I send mine to Freeborn) by a reputable shop I don't know how you would get stiles bowed at an angle. As for chatter, lube the table. I run blue wheels from Western Roller on the feeder. These grip the best. The ones that came with your feeder are junk. My guess is your chatter is caused by the feeder and/or the table.