'The Queen That Never Was' or 'The Queen Who Never Was'?

That used instead of who:

Research proves it isn’t quite the hard-and-fast rule one might imagine. For example, the indispensible Fowler’s Modern English Usage says: ‘That can also replace who (or whom), especially when the reference is non-specific, as in The person that I saw was definitely a woman.’ And examples of this usage can be found in work by Chaucer, Shakespeare and in the King James Version of the Bible.

(writing-skills.com)

That or who:

Most writers use that and which as the relative pronouns for inanimate objects, and who as the relative pronoun for humans. This widespread habit has led to the mistaken belief that using that in reference to humans is an error. In fact, while most editors prefer who for people, there is no rule saying we can’t use that, and that has been widely used in reference to people for many centuries. It remains so today, especially in British writing.

(The Grammarist)

And also from the AHD:

There is a widespread belief, sometimes taught as correct usage, that only who and not that should be used to introduce a restrictive relative clause identifying a person. But that has been used in this way for centuries, going back to the Old English period, and has been used by the finest writers in English, as in "The man that once did sell the lion's skin / While the beast liv'd, was kill'd with hunting him" (Shakespeare). and "Scatter thou the people that delight in war" (King James Bible).

In contemporary usage, who predominates in such contexts, but that is used with sufficient frequency to be considered standard, as in "The atoms in a diamond ... outnumber all the people that have ever lived or ever will" (Richard Dawkins). That also occurs idiomatically in reference to groups (where who would sound peculiar), as in "[She] had two sons, and settled into raising a family that soon included twin daughters" (David Freeman).

The English language seems to be changing. Google Ngrams shows that in the 1750s, "A person that" was used maybe a third as often as "A person who" (note that I start these with capital letters to avoid counting phrases like "to convince a person that"); while today, "A person that" occurs with the something like 1% the frequency of "A person who".

Is using that for people ungrammatical? It certainly wasn't in the 18th and 19th centuries, but it certainly seems to be headed that way, and you could probably make a good argument that it is today.

In my opinion, you should be very careful about calling things that were widely used 100 years ago "ungrammatical", as usages change with different frequencies in different dialects, and there probably are still some people who grew up in households and communities that used these constructions. However, I think we can safely say that you should avoid this construction—it will annoy or confuse a large number of native English speakers.

The Grammar Monster says

It is quite unfashionable to use that for people. (The consensus seems to be that using that for people is still acceptable in speech and informal writing, but you should avoid doing it in formal writing.)