I haven't yet seen or heard
The Minotaur, so can't comment specifically on that opera, but did have a few wider thoughts in terms of the issue of the 'maleness' of Birtwistle in general and the ensuing discussion. One factor being suggested for a particularly 'male' approach seems to be the use of 'archetypal' characters rather than sensitively-portrayed, complex, developing human beings. This is about the music as well as the libretto - the perceptions obtained about characters arise equally from the former. It seems to me as if this is really a debate about the relative merits of realist/non-realist approaches to opera and theatre (a subject we've been debating a bit on M&S recently, see
here; I'd also particularly like to draw people's attention to
this critical review by Terry Eagleton of Erich Auerbach's classic work of criticism privileging literary realism). That's not to deny that a realist/non-realist dichotomy mightn't have gendered implications, for sure, but I think it's worth locating this debate within that existing, highly developed discourse somehow.
For now, I'm considering Birtwistle's relationship to a long British theatrical tradition going back fundamentally to the Restoration*, as I see it, since when realist theatre of one type or another has been the dominant strain, right up to the present day. By this I mean a theatre that is focused upon characters, drawn with some depth and who are allowed to develop, in what seem like plausible situations (rather than surrealistic, fragmented, etc. narratives), also mostly focusing upon their external rather than internal lives, and adhering to a basically linear, coherent, and rounded narrative. I'm sure there are lots of problems with this definition, but it's the best I can do for now! The plays of Wilde and Shaw arguably push at the boundaries of this tradition but do not fundamentally break with it for the most part. The one time I see a genuine sustained break with the tradition is in the 1950s and 60s, with the highly Beckett-influenced work of Harold Pinter, and the more 'archetypal' theatre of Edward Bond; later writers such as Howard Barker and Sarah Kane continue some of this tradition, but were by that stage much more on the fringes of British theatrical life than their predecessors. Bond's profile receded significantly in subsequent decades; Pinter remained very much in the public eye, but arguably the radicalism of his later work has more to do with its subject matter than his approach to form.
Anyhow, I do see Birtwistle very much as one who came out of this relatively short-lived period of British modernism (from the late 50s until the mid 70s) and who in his operatic work took a very different approach to the character-dominated realist strain that dominated opera as well as theatre (including Britten and Tippett's, not to mention numerous later composers who came after Birtwistle). As others have said, his characters are mythical archetypes (I find that term more appropriate than 'stereotypes') rather than fully 'human' characters, who serve a functional rather than individualistic role within the work. This is certainly in keeping with various modernistic approaches to both genres, which move away from earlier forms of individualism, sometimes in the process drawing upon earlier theatrical or literary models. But it is very unusual within Britain. Evoking some forms of supposed primal experience, whilst using advanced modern techniques to do so, was a fundamental aspect of British/French/Italian/Russian modernism (Austro-German modernism frequently went in different directions, in various artforms). And allusion to or appropriation of myth (and an attempt to create para-mythical forms of musical experience) is one way to do this. I don't really see that this need be conceived as specifically gendered, unless one believes that all sorts of archaic culture (let alone contemporary ideals of them) are inextricably borne out of patriarchal societies and must be thus coloured - a perfectly reasonable position to take, of course; I'm really not sure if myths, many of which present female characters of all types (not just the locus of men's fears, though there is plenty of that) should be seen as purely the product of the minds of
men in the societies that bequeathed them, but I'd be interested to know what someone with a wide knowledge of anthropology would have to say about that.
Mythical subjects can be rendered in a realistic fashion, of course, and other composers have done so. But that is not really the case for Birtwistle. He joins a whole host of (mostly non-British) composers who have sought alternatives to character-based opera. There aren't really enough female composers of opera to be able to draw many conclusions about what an alternatively gendered approach might entail, though it might be possible to extrapolate something about the responses and preferences of listeners of either gender, though relative to time and place. Judith Weir has been mentioned (some might think that as a lesbian composer she is unusual; I don't really want to get into that); certainly her vaguely Brecht-influenced work is not fundamentally about the exploration of character in a realist mode either. Even the idea of myths as somehow presenting something 'timeless' (a point of view I certainly do not share) is not necessarily gendered (though it might be) - I can imagine there are a great many women who also hold to a comparable view (especially those who find positive feminist readings of myths and mythically-inspired drama, for example some Greek tragedy).
This is all a bit rambly (it's late); I suppose I'm asking whether a too-easy identification of certain aesthetic strategies with gender is at play here. There is an argument which associates a wide range of modernistic artistic developments with a entrenchedly gendered (male) ideology, to do with ridding culture of all elements perceived to be feminine (and also associated with 'the masses', themselves often conceived as feminine from the outside); this is not a view I share in its entirety, but also would not dismiss. If one did accept this view, it would be a small step to conceive not only Birtwistle, but also Boulez, Stockhausen, Xenakis, Scelsi, Cage, Feldman and various others as representing this type of modernism - essentially because of their tendencies towards abstraction as opposed to explicitly 'human' concerns (or conceiving the 'human' in a relatively abstract or archetypal form, as in the case of Xenakis in particular). But can we be so sure that the idea that women artists or listeners are primarily concerned with a more intimate 'human' type of art necessarily holds true? Let alone that these might imply that a realist approach is more 'feminine'?
Don't know if much of the above makes sense - interested in what anyone else might make of it.
*This is not of course to deny that realist elements existed in pre-Restoration British (or rather, at that stage, English) theatre - for example in Shakespeare - just to locate a point from which I think it became dominant.