"His people" are "those who are sanctified" by Christ, (Heb. 2:11).
Under the Old Testament, which was only a figure of the New, (Heb. 3:5), we could say, only temporarily, that "His people" were the descendants of Abraham according to the flesh, but that covenant, being weak, imperfect, and faulty, was cancelled (Heb. 10:9). Under the New Covenant, which is eternal, perfect and efficacious, His people are "the ones He makes holy." Those Christ sanctifies, Jew and Gentile alike, make up the house of Israel.
Both the one who makes people holy and those who are made holy are of the same family. So Jesus is not ashamed to call them brothers and sisters. - Hebrews 2:11 NIV
For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God. - Romans 2:28-29 KJV
It has always been so. Christ was not made a high priest after the order of Aaron. He was made a high priest after the order of Melchisedec, which was in operation in the days of Abraham, and was..IS, rather...a universal and eternal priesthood. Abraham paid tithes to Melchisedec, and so did Levi, as he was in the loins of Abraham, showing the priesthood of Melchisedec to be the true authoritative Priesthood.
I cited the verse in Matthew to show that "propitiation" is a removal of sin. Not a mere, temporary abatement of wrath.
Rom_3:25 whom God
set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed,
Heb_2:17 Therefore, in all things He had to be made like His brethren, that He might be a merciful and faithful High Priest in things pertaining to God,
to make propitiation for the sins of the people.
1Jn_2:2 And He Himself
is the propitiation for our sins, and not for ours only but also for the whole world.
1Jn_4:10 In this is love, not that we loved God, but that He loved us and sent His Son
to be the propitiation for our sins
Jesus's death on the cross did not remove sin but it did turn away the wrath for God from those that deserved it.
Propitiation
It is never used of any act whereby man brings God into a favorable attitude or gracious disposition.
It is God who is "propitiated" by the vindication of His holy and righteous character, whereby through the provision He has made in the vicarious and expiatory sacrifice of Christ, He has so dealt with sin that He can show mercy
to the believing sinner in the removal of his guilt and the remission of his sins. ...Through the
"propitiatory" sacrifice of Christ, he who believes upon Him is by God's own act delivered from justly deserved wrath, and comes under the covenant of grace.
He [God] can act differently towards
those who come to Him by faith, and solely on the ground of the "propitiatory" sacrifice of Christ, not because He has changed, but because He ever acts according to His unchanging righteousness.
The expiatory work of the Cross is therefore the means whereby
the barrier which sin interposes between God and man is broken down. By the giving up of His sinless life sacrificially, Christ annuls the power of sin to separate between God and the believer.
Vine's Complete Expository Dictionary of New Testament Words
The bible does not support your contention that "propitiation" is a removal of sin.