Romans 14:10-12 meaning

Living righteously looks like living in harmony with God's design. God intended that we live in harmony with one another through faith, not living in constant judgement over each other regarding religious rules. Focus on religious rules leads to condemnation and division. 

Paul points out the error in judging one another; we are not the true judges over righteousness and sin: But you, why do you judge your brother? Or you again, why do you regard your brother with contempt? For we will all stand before the judgment seat of God (v 10). 

We are here to lift one another up. There is a warning in these verses: Each one of us will give an account of himself to God, For we will all stand before the judgment seat of God. God is the ultimate authority. Indeed, verse 11 cites a prophecy detailing that everyone will one day be aware of God's sovereignty and give Him due praise (Isaiah 45:23):

For it is written,

"As I live, says the Lord, every knee shall bow to Me,
And every tongue shall give praise to God (v 11)."

If we remember that we will have to answer to God for our lives, we are in a better mindset concerning how to treat each other. With patience and understanding, even in disagreements of faith, whether one day is better than another, or a type of food is bad or good for an individual believer, it's better to encourage each other (Romans 14:1-9). We should avoid exercising our freedom in such a way that it might cause our brothers to fall into sin. 

Everyone will be judged one day by God (Romans 2:6). In light of that, we should minimize how often we judge other people's habits, and we should maximize living peacefully with one another. As Jesus instructed, when we see someone else sinning, our first decision should be to engage in self-examination, and root that sin out of our own lives (Matthew 7:3-5). 

Paul says in 1 Corinthians 4:3-4 that he is not aware of anything he is doing wrong, so he does not judge himself. However, that does not justify him, because he will have to answer to God for what he did in his life. 

This is a consistent theme for Paul, that God has the job of being judge of the world and of believers, so we should not usurp His authority in that respect. 1 Corinthians 4 occurs just after the chapter where Paul lays out the Judgement Seat of Christ, where every deed we do is judged by fire to test to see if it is a work that endures (1 Corinthians 3:11-15). 

Matthew 7:2 tells us that one of the measuring sticks that will be used to judge us at that great event will be the measure by which we measure others. So if we want to be judgmental and hold people to a high standard, then we will be setting that standard for ourselves when we stand before God in the judgement.

With this in mind, it is easy to see why Paul is adamant that judging other people is not in our best interest, instead each one of us will give an account of himself to God (v 12).

It is important to note that this is being expressed in the context where Paul has passed severe judgment on the false teaching of the competing Jewish "authorities." Paul warns against judging others' opinions. Truth is not opinion; Paul does not include truth here. The general exception to judging others applies to those who teach falsely or mislead others. 

However, even in regard to truth, Paul applies the standard to himself. After severely chastising the competing Jewish "authorities" who are attempting to mislead the Roman believers, Paul asserts:

"What then? Are we better than they? Not at all; for we have already charged that both Jews and Greeks are all under sin."
(Romans 3:9)

Paul readily admits that he too is a sinner. All have sinned, and all need God's grace (Romans 3:23-24). 

Other biblical verses where we are admonished to judge the fruit of others (such as Matthew 7:15-20) also refer to judging teachers and spiritual authorities so we know whom to follow. In this chapter of Romans, Paul's message applies to things that God leaves up to us to decide. But what God's word says is not a matter of opinion. And when people are being led astray, it is up to us to step in and call them out for it. This is for the false teacher's benefit as well, as Jesus said that, regarding anyone who misleads His children, "it would be better for him to have a heavy millstone hung around his neck, and to be drowned in the depth of the sea" (Matthew 18:6).