First, there were many areas of disagreement between them. It doesn't take having the Roman Catholic Church come around on every last one of them to make the point I did.
Sure, it wouldn't have to come around on every point. But it does require you to say which points you're referring to.
Second, I have already identified a number of issues where the RCC has more recently agreed with Luther's stands.
The only issues you seem to have identified are either liturgical ones (which I already mentioned) or the claim about throwing out deuterocanonical books, which will be addressed next.
Wrong! The RCC did not remove all of those books but she did remove some of them.
Even if this is an accurate description of what happened, this was done at the Council of Trent. So your claim that this was something "the RCC wouldn't consider in his [Luther's] own time" is incorrect.
I suppose someone could claim that the statement that "the RCC wouldn't consider it in his own time" but would "in more recent times" is sort of true because Trent's declaration of the biblical canon was given after Luther's death (by only a few months, though, I believe), which could qualify as being more "recent" than Luther's own time was. But that would be so pedantic it needs no real response.
That's wrong. While retaining a belief in "Purgatory," (which the church must do or else renounce the authority of the church council which created Purgatory), she has all but renounced it. This can be verified by consulting the Catechism or checking the words of the Pope himself and most any priest you know.
Let's check out the Catechism, then:
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1031 The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned. The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. the tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:
As for certain lesser faults, we must believe that, before the Final Judgment, there is a purifying fire. He who is truth says that whoever utters blasphemy against the Holy Spirit will be pardoned neither in this age nor in the age to come. From this sentence we understand that certain offenses can be forgiven in this age, but certain others in the age to come.
1032 This teaching is also based on the practice of prayer for the dead, already mentioned in Sacred Scripture: "Therefore Judas Maccabeus] made atonement for the dead, that they might be delivered from their sin." From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God. The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead:
Let us help and commemorate them. If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them.
How is this explicit statement of Purgatory a case of them having "all but renounced" it?
I don't know what you mean by "words of the Pope himself." Can you provide the "words" in question? I know that Francis has offered plenary indulgences. As for priests, last I checked, priests were still doing things like mass intentions for the dead, so there's Purgatory again.
The function, nature, and meaning of Purgatory now is nothing like the traditional view which the RCC taught for centuries.
In what way, exactly?