If Judgement is described as being “for the LIVING and the dead” as it says in modern versions of the BCP (both the Apostles' and the Nicene Creed), then it refers to those who are alive on that day and to those who have already died. In other words, the distinction is one of biology, that Christ, on the day of His return will judge not only those of us who are alive, but also those who dwell in the "after life", e.g. purgatory.
If on the other hand the Judgement is described as being “for the QUICK and the dead”, as it says for example in the 1662 Book of Common Prayer, then the distinction being made is between those that are alive (spiritually - the Elect) and those that are dead (spiritually - the Reprobate).
Scripture has a great many examples of Judgement between the Elect and the Reprobate, but it very clearly denies that God is constrained by biology. Nor does it describe the timing and location of Judgement other than to say:
1. There is a separation between "sheep" and "goats" in Eternity ("before all worlds"),
2. There is a separation made at the Cross, the "rock of stumbling" for some but the foundation of salvation for His chosen, and
3. There is a separation made at His coming again wherein this world is destroyed and "new heavens and earth" are created.
For this reason, it is only correct to say the Apostles' Creed (and also the Nicene Creed) with the traditional words "... to judge the quick and the dead", and if one were to modernize it, it would have to say something like "... to judge between the Elect and the Reprobate." It is a work of revisionist heretical dogma with implications of purgatory to say "... to judge the living and the dead."
There are MANY denominations that make this error, including those that are fervently Reformed. Thankfully, Reformed Anglicans who use the traditional liturgies are not exposed to it.