Getting grime out of non-skid is tough. The dilemma is that non-skid is not supposed to be slippery which means that it is going to hold dirt. So you don't want to put anything in there which is going to fill the micro pores, like wax.
I just take a deck
brush and scrub the heck out of it with boat
soap...and then try to ignore the deep ground in dirt that will never come out. You could also try acetone and a cotton rag to get the really bad stuff out. This works fairly well for relatively new gelcoat
. Acetone will not hurt gelcoat but will hurt a bunch of other stuff...so be careful using it.