I’m agnostic on the topic, thanks to the following concepts:
1.) “It is appointed for men once to die and then the judgment” – from Heb 9:27 (and on which I was composing an extended analysis a week ago, before last week’s deluge of ‘work’ work at work. Still continuing this week, btw… ) The gist of OT and NT teaching on the topic tends to synch up with this.
2.) The reincarnation of OT prophets is testified to in the Gospels as part of the popular belief of the time, not as authoritative teaching…
3.) …except that Jesus sort of affirmed it, too, when talking about JohnBapt…
4.) …but affirmed it in an oddly qualified way, difficult to translate (at least in Greek, whatever the original phasing may have been in Aramaic). “And, if you care to receive it, he even was Elijah”, or something like that. It certainly leaves open the question of the extent to which JohnBapt was supposed to be Elijah.
5.) On the other hand, George MacDonald was definitely willing to speculate along this line, both in his official theology (one or two refs in Unspoken Sermons) and in his fantasy work (The Princess and Curdie being the most obvious example of the principle); where the reincarnation serves a purgatorial purpose somewhat like it does for various forms of Buddhism or Brahmanism. (Sinners come back as non-human animals, in order to spiritually develop, not to say evolve, back to full humanity.)
6.) On yet the other hand, any theology (which I certainly affirm) that involves a bodily resurrection (in whatever mode), by default includes at least one incident of “reincarnation”, very strictly speaking. (Though apparently not in the sense of being physically born again, which reincarnation theories tend to feature. Though then again again again there’s the debate with Nicodemus in GosJohn chp 3. Nic was almost certainly engaging in a typical rabbinic habit of showing their rejection of an idea by rephrasing it in the most offensive manner that occurs to them, but Jesus, especially in GosJohn as later with the whole flesh-munching episode, has a habit of turning that tactic back around by revealing that, as a matter of fact, He does mean literally that, in a way, sort of! )
So, eh. I can take it or leave it, but I don’t have to have it. But scripturally speaking, I would not be expecting it, except at the general resurrection in some way. So I’m much closer to denying it than accepting it.
(There are, however, a lot of weird things in the world, so I’m leery of outright denying it, too. )