The confusion comes in thinking the animal sacrifices somehow made it possible for sinners to go to heaven when they died. That was NEVER their purpose. Their purpose was to allow sinners to enter the EARTHLY presence of God at the Temple.
I agree with the notion concerning going to heaven (the next life). However the people did not enter the presence themselves as they were not allowed into the temple. But it did provide for priestly representation before God. The common people were themselves estranged from God's house.
Nu 1:51 And when the tabernacle setteth forward, the Levites shall take it down: and when the tabernacle is to be pitched, the Levites shall set it up: and the stranger <02114> that cometh nigh shall be put to death.
Nu 3:10 And thou shalt appoint Aaron and his sons, and they shall wait on their priest’s office: and the stranger <02114> that cometh nigh shall be put to death.
Nu 18:4 And they shall be joined unto thee, and keep the charge of the tabernacle of the congregation, for all the service of the tabernacle: and a stranger <02114> shall not come nigh unto you.
Nu 18:7 Therefore thou and thy sons with thee shall keep your priest’s office for every thing of the altar, and within the vail; and ye shall serve: I have given your priest’s office unto you as a service of gift: and the stranger <02114> that cometh nigh shall be put to death.
02114 זור zuwr zoor
a primitive root; v; [BDB-266a, BDB-266b] {See TWOT on 541}
AV-stranger 45, strange 18, estranged 4, stranger + 0376 3, another 2, strange woman 2, gone away 1, fanners 1, another place 1; 77
1) to be strange, be a stranger
1a) (Qal)
1a1) to become estranged
1a2) strange, another, stranger, foreigner, an enemy (participle)
1a3) loathsome (of breath) (participle)
1a4) strange woman, prostitute, harlot (meton)
1b) (Niphal) to be estranged
1c) (Hophal) to be a stranger, be one alienated
the significance of this nuance concerns (Eph 2) the Messianic priesthood and sharing in the sacrifice of the priesthood. No zuwr could eat of the priestly meal either.
Le 22:10 There shall no stranger <02114> eat of the holy thing: a sojourner of the priest, or an hired servant, shall not eat of the holy thing.
Le 22:12 If the priest’s daughter also be married unto a stranger <02114>, she may not eat of an offering of the holy things.
Le 22:13 But
if the priest’s daughter be a widow, or divorced, and have no child, and is returned unto her father’s house, as in her youth, she shall eat of her father’s meat: but there shall no stranger <02114> eat thereof.