On my 2014 CB500F there is not much passenger seat movement front to rear when the seat is properly inserted into the bike. I measured mine = 3/16 inch.
I was more worried about the side to side movement when carrying a passenger. I glued shims to the sides of the two prongs that project forward underneath the seat and hook under the chassis. The shims reduced the side to side movement considerably. It's roughly 1/8 inch now.
Used urethane glue to be sure my shims would stick to the rubber parts.
2014 CB500F: GSXR600 rear shock, Traxxion fork emulators+springs, Kuryakyn Throttle Boss, IDEA Gear Indicator, Puig Wind Screen, SW-Motech handlebar risers, LED tail light, rubber tank side pads.