I had the same issue with my 2010 ultra classic. I changed over to redline synthetic and no more problems.

 

Just bought an 03 Sportster 883 Standard with 18k on it. I assume it's been sitting for at least a couple months if not longer. It was a younger guys first bike. His gf didn't want him having it (she said he's too clumsy). It has the original tires on mags from 03. I'm having issues with getting into neautral as well. I'm planning on changing all fluids and hopefully that will help along with a clutch adjustment. After reading I believe this will soften the issue. I will post back after work is completed for future reference.

 

Same here.. I put in Redline 85-140 with shockproof and shifting and finding neutral improved to perfect. Smooth as butter now.

 

Hi Jeff,
Yeah, sometimes it can be a bitch to find neutral.
I’ve got a 2014 Iron 883. I found it especially challenging if I’m wearing sneakers or some other kind of light footwear. When I wear boots or footwear made of some firm leather or other thicker material it’s much easier.
Check it out.
Be safe.
Greetings from Belgrade, Serbia.

 

That is certainly the right way to go. New tyres, new fluids, new bike - all being well! If you don't have one the factory service manual will help you do what is needed.