Different journals have different standards of rigor. I believe Physics Letters B, where this paper was published, is one of the less rigorous ones. They might also be more inclined to publish speculative papers, figuring that it's better to publish it and let someone else publish a refutation if it's wrong, as opposed to refusing to publish it in the first place.

In this case I think you're saying the paper itself should not have been using isotropic coordinates.

I suspect that the use of isotropic coordinates misled the paper's author, yes. I can't know for sure since I can't read the paper itself (it's behind a paywall). [Edit: someone downthread posted a link to an arxiv preprint; I'll take a look and respond further there.]

Is this because of different schools of thought in this higher realm of physics?

This could be a factor--it certainly is in some cases--but I'm inclined to think that in this case it's more a matter of a less rigorous journal being willing to publish a speculative paper, as above.

That sounds familiar.

No, they don't; I think you're thinking of Schwarzschild coordinates. Isotropic coordinates are continuous at the horizon, which is at R = M/2 (where R is the isotropic radial coordinate and M is the mass of the hole); but the region R < M/2 corresponds to the exterior of the horizon, not the interior.

The standard interpretation of this is that isotropic coordinates double cover the same exterior region (which is labeled region I on a Kruskal diagram like the one in Figure 2 on the ScienceDirect page); in other words, for every value of R < M/2, there is a corresponding value of R > M/2 that labels the same point in the same exterior region.

Poplawski's paper appears to claim that there is a valid alternate interpretation in which the region R < M/2 is a second, separate exterior region (labeled region III on a Kruskal diagram). That interpretation appears to me to violate the Einstein Field Equation, but I'm still digesting the paper (see my other posts in this thread).