Hey, I'm wondering if the rubber rings in the clutch can cause clutch drag and or a very stiff pull? New cable, push rod is straight, and the push mechanism is free

If by drag you mean sitting in gear & it's trying to pull you along & can't find neutral easily then it's a slight possibility because those rings sit under the fibers & any oil around them 'could' act to pull the plates around. that's really splitting straws though so probably not the problem. If you are in there then take them out anyway.Stiff pull i dunno but what i do & i saw it said on another post--feed the cable as freely as you can & in gentle curves up to the lever. If the actuator is lubed then that's good. They do split the nylon worm which forces thing out tight in the worm outer when pulling the lever so that needs changing if split. Slacken the adjusters & adjust the pushrod screw to bring the arm as far down as possible with a little clearance. Then take up the cable play on the adjusters, Some accessory aftermarket levers have more pull with a different pivot point so keep that in mind. Sorry i'm assuming 250 or 360 but if 175--125 the same applies except for a split actuator. On one of my rat bike fleet i'm running the cable on the outside of the tank in a big curve & is great. Might be a short cable i found & had to do it. Not recommending that but could try it as an experiment.
One more thought in a day of random thoughts. Be sure your clutch hub is free to turn without plates fitted. Many times i've had tight hubs from probably minimal clearance in the first place, then after people have had it apart a couple of times & tightened the center nut with a powerful rattle gun, the washers get slight dents from the spacer they sit against & its enough to tip the balance between free & binding up. Unlikely i know--but!!

Thanks 325!