What did the ancient Celts really believe and practice?

The short answer is that we don't really know for sure. And that modern attempts to reconstruct this lost tradition are always going to be based on modern assumptions and opinions rather than anything genuinely representing the ancient Celtic wordlview.

The problem we have with ascertaining authentic ancient Celtic beliefs and praxis basically boils down to:

(1) Lack of primary sources from the Celtic point of view due to both the wholesale Roman conquest of Celtic territories and the fact that Celtic spirituality was an oral tradition; very little was written down.

(2) Highly-biased second and third hand accounts of their beliefs and practices from parties who were rather hostile to (or just ignorant of) Celtic traditions.

(3) The fact that at their peak, the Celts were not a single nation or centralized political entity, but rather a continuum of various tribal groups and confederations that spanned a rather large geographic reach. And owing to this decentralized arrangement, there would have been quite a variety of differing beliefs and practices found among the varying groups spread out over this vast expanse of land; of course all of this was held together to some degree by the Druid orders which did bring some semblance of coherence to the whole thing, despite the many local differences in religious expression. But let us not pretend for one moment to know what the Druids believed or taught.

The same three points above could applied to other tribal traditions that the Romans wiped out, whether that would have been through direct military conquest or the later-occurring religious conquests of Roman Christianity via its mass conversions of various European peoples.

We can clearly see now why the many attempts at pagan reconstruction today constitutes an ever-precarious endeavor.

Second-hand Pseudo-Traditionalist smoke

In my internet travels, I have noticed that the so-called Traditionalist School (Guenon, Schuon, Evola, ect.) has produced a small (but dedicated) cult following of pseudo-intellectual repeaters who faithfully parrot the general sentiments and select talking points the original authors like Rene Guenon, Frithjof Schuon, Julius Evola, ect., expressed many decades back. Many of these followers are simply devout adherents of sectarian religions looking for a metaphysical and intellectual rocket-booster for their particular set of beliefs. Take this commentator as an example, as he attempts to write-off the ancient Pythagorean-Platonic lineage of classical antiquity as something that should not qualify as what he personally considers to be a "tradition" based on his own Confucian-style readings of the aforementioned authors.

You ask about “independent sages”. The only person I can think of whom the perennialist authorities would regard as a genuine master, but who seems to have been unaffiliated with any revealed tradition, is Plotinus. One recalls his response to Porphyry’s suggestion that he attend a Christian liturgy, since there would be angels there: “It is not for me to go to those beings, but for those beings to come to me!” He, and perhaps a very few others, are exceptions that prove the rule.

Though one must of course grant that such a possibility exists in principle, it is nonetheless obvious that a man is a fool if he refuses to take advantage of the sacramental protection of an orthodox tradition on the grounds that he might himself be among so selective a group. Those who suppose themselves the equals of a Plotinus, with angels running up and down the ladder of their being, would be well advised to ponder Schuon’s admonition: “Metaphysical intuition alone does not prevent titantic falls.”

It is one thing to have glimpsed certain truths, and even to be able to convey them to others; it is something altogether different to be wholly transformed by these truths—to know That Which is by virtue of having become That which knows. Don’t make the mistake of equating a planimetric understanding with a truly global realization.

IMHO the problem here is that the author implicitly states that he only considers a very limited number of "revealed" doctrines of middle eastern origin to be "orthodox traditions." And by "revealed creeds of middle eastern origin," I mean the more dogmatic of the Magian religions of Near East that Oswald Spengler referenced in his eminently-profound work "Decline of the West."

The commentator I quote above conveys either a misunderstanding or willful misrepresentation of the Tradition sages like Iamblichus, Plotinus, Porphyry, Ammonius Saccas, Plato ect. hailed from, which was at least 700 years (at the time of Plotinus) of sacred teachings passed down in an unbroken teacher-disciple line. On the other hand, Christianity at the time was still a very young, new religious movement. If we were to apply 20th century "Traditionalist" rhetoric to this particular time period in late antiquity, then it would be Christianity that would be considered the upstart, possibly "inauthentic' religion (unless of course it followed Jewish tradition to the letter), not the Pythagorean-Platonist schools, which would in fact be a firmly established Tradition of the Hellenistic world.

Basically this "independent sages" label being applied in this situation is quite nonsensical and reeking of sectarian solipsism. It's also a straw man. I would wager with the best of my thinking abilities at this particular time that, like all devout Judeo-Christian apologists, the commentator's imperative is to defend and promote his particular version of religion.