‘Follow after (‘pursue') peace with all, and the sanctification without which no man shall see the Lord.'
Some see this as meaning ‘all men' as in Romans 12:18, but the context rather suggests it means all their fellow Christians with whom at present they are not perhaps fully at peace because of their Judaistic tendencies. They should seek to be aligned with them in their beliefs and hopes. But whichever way it is, ‘Blessed are the peacemakers for the they will be called the children of God' (Matthew 5:9). Those who are His seek peace with all, and peace between all, for that is how God's children should be. And this should be accompanied by following ardently after ‘sanctification', that sanctifying process whereby they are being conformed into the image of Jesus Christ (Romans 8:29), for in this they will have peace with God. It is peace to be achieved within sanctification. We must never seek a false peace which is not accompanied by sanctification. Oneness is important, but never at the cost of holiness or truth.
‘Without which no man shall see the Lord.' ‘The Lord' here probably means ‘Jesus Christ' rather than ‘God', for outside of quotations this is how the writer usually uses the title (Hebrews 2:3; Hebrews 7:14). Thus ‘seeing the Lord' here probably refers primarily to His second coming (Hebrews 9:28; 1 John 3:2-3). It is a reminder that if we are to see Him we will at present be experiencing His sanctifying work (Hebrews 2:10-11).
However, as Jesus Himself said, ‘Blessed are the pure in heart, for they will see God' (Matthew 5:5) and there He was surely including the experience of this ‘seeing God' as being available at the present time, in the new age of the Kingly Rule of God which had come in Him. He is saying that it is only if our hearts true that we will see Him. For it is only if we are at peace with one another, and experiencing constant sanctification, if we are genuinely pure in heart, that we can see Him (compare Hebrews 12:2). Then we can experience the vision of God now in our hearts and spirits. Yet glorious though such a thought is, it is a but foretaste of what will be ours in fullness when we see Him face to face. We may see Him now in our hearts, and His beauty may shine on us, a beauty of which we can only have a relatively minimal idea, but then we shall see Him in His fullness, we shall see Him as He is (1 John 3:2). We shall see the King in His beauty (Isaiah 33:17). We may be being conformed to His image now, but then the process will be complete. Then we will be made like Him, for we will see Him in all that He is (1 John 3:2-3).