So they will be saved at some point at which they no longer believe false doctrine. What's the difference?
Your view is wretchedly fatalistic, full of human reasoning and against the word of God. He says,
'All authority has been given to Me in heaven and on earth. Go therefore........' (Matthew 28:18-19). If all authority has been given to Christ, why do we need to do anything? His will is going to be done in any case so let's sit back and let Him get on with it! When William Carey first suggested a mission to India, an elderly minister is supposed to have said to him, "Young man; sit down! When it pleases God to save the heathen he will do so without your help or mine!"
But this view is desperately earthly. It is precisely
because God is utterly sovereign that we are to go!
"Go therefore and make disciples." The God who declares,
"I will have mercy on whomever I will have mercy" (Romans 9:15) and decreed salvation for a vast crowd of sinners has also decreed the means of their salvation- the Gospel of Jesus Christ faithfully preached. They will not be saved without hearing the Gospel (Romans 10:14-15). And that is why David Brainard, dying from Consumption, forced himself through the American wilderness to reach the Red Indian tribes and bring the Gospel to them. He was a five-point Calvinist, but he wanted to see God's name glorified among the heathen.
Today, people are perishing because of a false gospel. We don't know who is elect or who isn't and that should not be our concern. Our concern should be the glory of God!
'For the name of God is blasphemed among the Gentiles because of you' (Romans 2:24).
'Whatever you do, do all to the glory of God' (1 Corinthians 10:31).