It looks like you need to plane it anyway!
From that picture, it looks like that post has a lot of surface damage. Has it rattled around in the back of a pickup on the way home, to pick up all those dents and scratches? If you're worried about how it'll look, I think those should be your first thing to worry about, not a bit of superficial dirt! And considering how comprehensively battered it seems to be, you'll need to run a plane over each side to sort those out - which as other comments have said, will naturally take off any dirt along with that thin layer of wood.
If you'd taken good care of your materials though, you could...
Use oil to treat the wood, and don't worry too much about marks
If you're planning on applying polyurethane varnish or waterproofing woodstain then clearly you need a clean face on the wood before you apply it. Softwood is most likely to need this, because you need to keep water out of softwood to stop it rotting. (Based on the damage I can see, I suspect this may be what you've got?)
If your "redwood" is cedar or other rot-resistant hardwood though, generally you would use an oil-based treatment on the deck. The first step before treatment is to scrub off dirt with a tough brush, and that will naturally shift most of those marks. Any residual dirt on the wood simply fades over time, either by the dirt washing off, or the top fraction of a millimetre of wood slowly eroding with wear, or when you scrub it again next year to re-oil it.