>This article covered more than I was expecting, but still manages to squeeze a small amount of substance into a relatively large article. Here's a tl;dr:
- Penrose and Hameroff postulate microtubules might have quantum mechanical behavior in their Orch-OR hypothesis. This hypothesis was refuted by Max Tegmark in the 90s. Penrose doesn't care and keeps preaching his hypothesis, and has not put forth any new scientifically compelling arguments in the past 2 decades.

"Doesn't care" as in la-la-la hands-in-the-ears, or doesn't care as in, believes the refutation is not valid, or believes that despite the refutation of that particular mechanism there's enough evidence that there's another related mechanism?

Here's how Wikipedia puts it, which is not at all as "Tegmark won", but rather like "Tagmark's claims were wrong themselves, and refuted further":

In response to Tegmark's claims, Hagan, Tuszynski and Hameroff[56][57] claimed that Tegmark did not address the Orch-OR model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, although still far below 25 ms. Hameroff's group also suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding actin gel might enhance the ordering of water, further screening noise. They also suggested that incoherent metabolic energy could further order water, and finally that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of resisting quantum decoherence.

Since the 1990s numerous counter-observations to the "warm, wet and noisy" argument existed at ambient temperatures, in vitro[23][42] and in vivo (i.e. photosynthesis, bird navigation). For example, Harvard researchers achieved quantum states lasting for 2 sec at room temperatures using diamonds.[58][59] Plants routinely use quantum-coherent electron transport at ambient temperatures in photosynthesis.[60] In 2014, researchers used theoretical quantum biophysics and computer simulations to analyze quantum coherence among tryptophan π resonance rings in tubulin. They claimed that quantum dipole coupling among tryptophan π resonance clouds, mediated by exciton hopping or Forster resonance energy transfer (FRET) across the tubulin protein are plausible.[61]

In 2007, Gregory S. Engel, Professor in Chemistry at The University of Chicago, claimed that all arguments concerning the brain being "too warm and wet" have been dispelled, as multiple "warm and wet" quantum processes have been discovered.[60][62]

In 2009, Reimers et al. and McKemmish et al., published critical assessments.[19][37][45] Earlier versions of the theory had required tubulin-electrons to form either Bose–Einsteins or Frohlich condensates, and the Reimers group claimed that these were experimentally unfounded. Additionally they claimed that microtubules could only support 'weak' 8 MHz coherence. The first argument was voided by revisions of the theory that described dipole oscillations due to London forces and possibly due to magnetic and/or nuclear spin cloud formations.[6] On the second issue the theory was retrofitted so that 8 MHz coherence is sufficient to support the whole Orch-OR hypothesis.

McKemmish et al. made two claims: that aromatic molecules cannot switch states because they are delocalised; and that changes in tubulin protein-conformation driven by GTP conversion would result in a prohibitive energy requirement. Hameroff and Penrose responded to the first claim by stating that they were referring to the behaviour of two or more electron clouds, inherently non-localised. For the second claim they stated that no GTP conversion is needed since (in that version of the theory) the conformation-switching is not necessary, replaced by oscillation due to the London forces produced by the electron cloud dipole states.