What would you say is the mark of authentic Christian esoterism?
Any teaching that can evidence its roots in the Tradition.
The Fathers' disputes with the 'Gnostics' is a case in point, and I'm probably more open to Gnostic speculation now than I was, but still regard much of its as interpreting the Christian Tradition is view of pre-existing assumptions – that it was not Jesus who was crucified but another, possibly Judas, or that Jesus was an angelic being who only appeared human, and hence could not suffer, etc.
The idea of two separate and distinct streams of Christianity – the visible exoteric Petrine stream, essentially 'dead in the water', and the invisible and esoteric Johannine stream – the latter, of course, being the province of the 'esoteric schools' ...
It's a fine line ... I observe a distinction between 'esoteric Christianity' (a pseudo-esoterism) and 'Christian esoterism' (which isn't) – in the same way as speaking of Platonic Christianity, as opposed to Christian Platonism – the distinction being who takes the superior place in the discussion – Christian principles according to a Platonic perspective will arrive at a different place than Platonic principles according to a Christian perspective.
An example of the latter is St Maximus' correction of the errors of 'Origenism' (and not necessarily Origen).
More pointedly, Maximus revised the Platonic model of rest-movement-becoming (stasis-kenesis-genesis) (the eternal state of souls, stasis, satiated by the Divine Gaze, move, turn or fall away, kenesis, and the world is created, genesis, to catch the spark of the soul in its descent, simply by turning it on its head, as given in Scripture, so its genesis (from non-being to being) and the movement towards rest (stasis) in God.
How much syncretism is there in Christianity, that's considered authentic enough?
Again, much like the Perennialists, I try and discern between complementary truths that manifest themselves in particular forms in the various traditions, as opposed to a rather blanket assertion that 'all religions say the same thing' (they clearly don't) and that any particular element of any religion can be shaped to conform to any and every other.
Therefore I see pagan rituals, those based on the natural rhythms of season and zodiac, etc., as being 'absorbed' into Christianity without offence to either – much like symbols that carry universal and particular meanings ...
Whereas perhaps the Christian habit of clothing itself in the trappings of Roman Empires can be understood, but with as much sadness with regard to what was surrendered, as charity towards what was assumed.