God knows who the non-elect are .
I don't think anyone has an issue with God knowing/foreknowing who the non-elect are. If He Himself chose the elect, He'd quite obviously know who the non-elect are. The issue is over whether God predetermines/predestines the non-elect to condemnation by His determinate counsel even before the foundation of the world - or not.
Scripture to support the predetermined/predestined condemning of the non-elect has been limited to just Rom 9:17-23 - if there are more passages elsewhere, please cite them. But if this is the only passage on which double predestination has been based on, then there should be reconsideration to its interpretation.
The entire passage deals with all being utterly dependent on God's mercy alone. Now, the very concept of mercy comes up only after one is consigned to condemnation, not before - for how can one be shown mercy if he has done nothing guilt-worthy to be condemned in the first place. And once a person finds himself in that state of condemnation dependent on just God's mercy, he is no longer entitled to anything - God is sovereign and is not obligated to show mercy to this person. If God so does show mercy, this person shall have eternal life in accordance with God's will - if God does not show mercy, this person shall face God's just wrath for his own guilt-worthy transgressions.
It is in this sense that it is written, from the same lump one is made unto honour and the other unto dishonour. If you want to read double predestination into this, you'd read it as "from the same lump of mass before one's birth" - but if you don't want to read double predestination into this, you'd read it as "from the same lump of guilty condemned people after their own transgressions".
Moses and Pharaoh are both transgressors before God, both deserving condemnation in accordance with God's Law. It is at this point that God sovereignly chooses to have mercy on Moses and not on Pharaoh - resulting in Moses being sanctified to walk as per God's will and Pharaoh drifting further apart, for God's mercy begins His good work in His vessels of mercy unto honour. But there is God's longsuffering to withhold His just wrath towards Pharaoh until his sins are finished (James 1:15) and he is completed for destruction.
The expected objection is why God 'still/furthermore/yet' finds fault - not over why God found fault in the first place. Why does God find fault with people's disobedience when He has sovereignly willed them to be vessels of wrath (after first their transgressions amounting to their condemnation and God not willing to show mercy upon these). For If God had willed them to be vessels of mercy, then wouldn't they have been spared God's just wrath - so isn't it unfair to hold them responsible for God's decision. Which is what Paul defends by saying God is entitled to make that sovereign choice of whom to have mercy upon, given that all are the same lump of equally undeserving transgressors.
And note, it is the vessels of mercy that are "afore prepared unto glory". It would be our assumption to extend the same to the vessels of wrath when Scriptures make no such mentioning.
All this is to show that the doctrine of single predestination would conform to Scriptures while double predestination is a result of human assumptions. I'd think people should be happy to reject double predestination at the first instance of a biblical reconciliation without it, given its implications of a God who weeps for the perishing of the very people He intentionally created to perish.
