I heard again recently the former Priesthood ban justified as being God's will because it was similar in nature to the restrictions established with the Levitical Priesthood in the Old Testament.  Once again, I cringed.  
We must stop trying to justify the ban by citing justifications that existed and were used prior to the ban being lifted in 1978.  There are too many statements by prophets and apostles since that date that have told us that all previous justifications were incorrect for us to continue to use them.  (
If anyone who reads this wants to see some of those statements, search under the label "Race" near the bottom right of this blog.)  
As to the claim, the following is my response: 
1) 
EVERY
 instance in our canonized scripture of such a restriction, if it 
existed, occurred prior to the ministry of Jesus Christ. Look it up: 
Every reference is from before he ministered among the Jews. I believe that simple fact
 is critical to understand as the foundation of the discussion. Thus, if someone
 posits that there were “bans” based on lineage or race prior to the 
modern one, they have to admit that those bans appear to have stopped with Jesus’
 ministry – according to our scriptural canon.
2) There are 
NO recorded revelations justifying the modern Priesthood ban. 
ALL
 of them used the Old Testament time period justifications that were 
common within “apostate” Christianity at the time. Think about that aspect of the discussion – that 
the justifications were borrowed from denominations that we classified as “apostate” at the time. It’s instructive, I think. 
2)
 Jesus’ statement in Matthew 15:24 about being sent only to the lost 
sheep of the House of Israel says absolutely nothing about the 
Priesthood. It refers only to his ministry – his preaching, healing 
and blessing. The woman in question wasn’t asking for the Priesthood; 
she was asking that He perform a miracle on behalf of her daughter. 
Thus, 
that passage is completely irrelevant to the modern Priesthood ban and any other similar ban.
3)
 The last message Jesus gave his disciples in Matthew before his 
ascension is recorded in Matthew 28:19-20, which reads (emphasis mine):
“Go ye therefore, and teach ALL nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe ALL things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.”
Notice, they were commanded to teach and baptize 
ALL
 nations (which doesn’t address a Priesthood ban, since even under the 
modern ban, all people could be taught and baptized), but notice that 
once 
ALL were baptized they, without exception, were to “
observe ALL things whatsoever I have commanded you”. In other words, there is 
NO restriction of 
ANY kind on what 
ANYONE
 who was baptized was required to observe – and all members at that 
time couldn’t have followed that commandment without the Priesthood being given to them. 
Thus, by default (
not reading into the passage what isn’t there), there was no Priesthood ban in the early Christian Church that was based on nationality or race.
4) Nephi (a prophet from the Old Testament time period) passed along the idea of a curse in his writings, but the Book of Mormon also has 
NO mention of it after the visitation of Jesus in 3rd Nephi. 
It ended, if there was one, with the ministry of Jesus among them.
 Furthermore, Nephi undercuts the idea that the curse he mentioned was 
skin- or lineage-related when he said in 2 Nephi 26:33 (again, emphasis 
mine):
“For none of these iniquities come of the Lord; for he 
doeth that which is good among the children of men; and he doeth nothing
 save it be plain unto the children of men; and he inviteth them ALL to come unto him and partake of his goodness; and he denieth NONE that come unto him, black and white, bond and free, male and female; and he remembereth the heathen; and ALL are ALIKE unto God, both Jew AND Gentile.”
Nephi says in that verse, explicitly, that black and white are “
alike unto God” – and that God invites 
ALL to “
come unto him and partake of his goodness”.
 People who are partaking of the same goodness and who are alike unto 
God eliminates, obviously and unequivocally, the idea that one group 
held the Priesthood and could attend the temple while the other group 
didn’t and couldn’t. The ban makes 
NO
 sense whatsoever when read according to that verse – and it was written
 before Christ’s ministry. If that verse is interpreted literally, and 
if there actually was a race-based Priesthood ban at some point in 
history, it had ended by around 600 BC – or, if read to coincide with 
the ministry of Jesus, it ended at that time, at the very latest.
5)
 The issue with the Gentiles in the early Christian Church wasn’t about 
Priesthood or the temple in any way. At least, there is 
NO mention whatsoever of the Priesthood in any passage dealing with the issue. It was about baptism, and once the Genitles were baptized, there is no reference to any of them not receiving the Priesthood based on race.
6) To add something that I almost never hear discussed or even recognized, there's a 
HUGE conceptual difference 
between the following: 1) giving 
one group in a "multi-tribal" population the 
right to perform rituals; 2) giving 
everyone except one specific group in a "multi-racial" 
population that right
.  In very real, practical terms, the modern ban was the exact opposite of the ancient Levitical structure. 
7) Joseph Smith ordained multiple black men to the Priesthood, so 
it’s patently absurd to argue that he believed a ban was necessary – regardless of how he felt about any other bans that might have existed in the past.
Conclusion:
Based on our actual scriptural canon, 
even if some bans actually did occur in the Old Testament times, there is 
NO
 evidence that any ban continued after the ministry of Jesus Christ – in 
either the Bible or the Book of Mormon. In fact, there are multiple 
sources that imply or state explicitly that a ban from that point onward
 was not the will of God – that 
ALL people everywhere now were considered “
alike unto him”.
Finally, the LDS Church has published a statement entitled, "Race and the Priesthood" that can be found on lds.org in the Gospel Topics section that states more clearly than ever before how the ban originated and how the leadership views it now.  The link is:
"Race and the Priesthood" 
So, if even our modern prophets and apostles say the former justifications were incorrect (“
spectacularly wrong”,
 in one quote) – and if even they say they don’t know exactly why the 
ban was implemented (with which I can’t argue strongly, since I think 
it’s obvious but am willing to admit that I can’t see 100% into Pres. 
Young’s mind and know with total certainty why he did what he did) – and
 if they are saying forcefully that we should not perpetuate the former 
justifications – and if even they now have said that the Church condemns
 
ALL racism of any kind, including that of our own LDS members, past and present – and if 
ALL
 the written evidence since the time of Jesus’ mortal ministry points to
 the incorrectness of a Priesthood ban (especially based on one drop of 
blood from a long-ago ancestor – who, by the way, is a common ancestor to 
ALL of us, if the “
one drop”
 standard is used) — how can someone possibly argue that the modern 
Priesthood ban was justifiable based on the beliefs of those who lived 
and recorded their beliefs before Jesus was born, 
even if previous bans existed and were justifiable back then?
Such a position simply is not tenable, and, just as importantly, it is in direct opposition to our current leadership and their requests of us.  That, perhaps, is the ultimate irony in the justification being used  today by someone who believes in "following the prophet".