My hair is dead straight, blond & fine, so this is something I've worked out over many years of similar issues.
If you have long hair then it cannot possibly be getting greasy right to the ends in a couple of days unless you brush it like an old Victorian school teacher, 100 times before bed.
Hair has 'scales' - as they love to show you in all the shampoo adverts. Shampoos & conditioners' job is to smooth these 'scales', curing all kinds of percieved issues such as 'fly-away' hair etc. They do this using silicones, which coats each hair to flatten the scales, reduce static build-up & provide a non-grip shiny surface, like a teflon pan. They also help to reduce friction & therefore will detangle your hair easily… thing is, dead straight fair hair doesn't actually really tangle all that much anyway. Mine used to be well past shoulder length & still didn't.
If you have really fine hair which really needs more 'body' then you actually don't want this scale-smoothing, slippy effect, otherwise your hair ends up looking flat & greasy. It's no more greasy than anyone else's, it just doesn't retain body, which makes it look & feel limp & by association, greasy.
So, try an experiment.
Wash your hair with washing-up liquid [dish soap]. This should strip oils [& eventually the silicones] without replacing them with more silicones that shampoos contain. Don't worry, it won't kill your hair, washing-up liquid these days isn't as vicious a grease-cutter as it used to be, because it's "kind to hands".
Rinse the soap out, then instead of conditioner, use a bath salt mixed in warm water [not a liquid bubble bath type, a box of powder] - I use Radox simply because I like the smell; you don't need anything expensive. Don't make it too strong - the mix on this you might need to experiment with. The more you use, the 'dryer' the result.
Rinse again in clean water, dry as normal.
The action of those will actually lift the scales on your hair & make it appear thicker. It will also be resistant to looking greasy because of the scale lift.
Note that it may take a few attempts at this before you manage to get rid of all the silicones the regular shampoos have in them.
If you ever think it's gone too far the other way, too dry, try one wash in just shampoo; because this method is not adding anything that one rinse in plain water won't remove.
If the method still feels a bit 'greasy' after maybe a couple of weeks of this method, then next time don't rinse the bath salts out, leave that as your rinse stage.
If you need even more body, then use a matt paste styling product. I use Label M matt paste, after many years' search for a good non-shiny, non-greasy product, but I'm sure there must be others that will do the same job.
I now only wash my hair once a week using this technique & it really doesn't look greasy in between.