I haven't really delved into a lot of in depth Olikan 'doctrine' yet, but this is where we're getting into the complexity of different interpretations of core Olikan tenets by different philosophical schools, societies, and individuals. At its heart, Olikan faith is exactly that, a henotheistic universalist faith that believes not only should all Gods as understood by different cultures be worshipped but all of the such Gods *must* be worshipped. However, there's quite a lot of room for interpretation as to exactly how one goes about that. Some place high importance on the survival of existing temples and centres of worship, and will seek to revive a disused or abandoned sacred site if they have reason to believe that's what they've encountered. Others, however, believe it's basically enough to build a Pantheon that in theory represents all Gods anywhere and everywhere, with imagery to match, so that local, indigenous, and older houses of worship are not particularly important. In later eras there are those who don't believe any sort of sacred structure representing the 'house' of a deity is required whatsoever. Some believe that the correct cultural context around a deity is important, as extended from knowledge of liturgical languages, whereas other see it purely as a matter of acquiring enough information about deities to maintain worship of them after the underlying culture has been 'civilized'.
What we are encountering in the specific example of the Italic peoples is the disconnect between a set of principles applied in their most altruistic form versus how that can be applied in situations with massive power disparities. A codified spiritual belief in heterodoxy and universalism does not preclude one from being chauvinist, xenophobic, or from falling victim to imperialist teleological worldviews. In the specific case of Irmion, he believes very strongly in the maintenance of deities from across the world, but also has a worldview in which peoples can be more or less civilized, and that those cultures that continue to exist in his present time do so because they deserve to. As far as he's concerned the minute people had sufficiently accounted for the deities and sufficient of the practices of a given 'barbaric' culture they could all drop in a volcano. 'You don't understand the nature and power of this cultural repertoire you possess, we'll be making sure it's preserved so the world has no need of you in order for these things to continue existing. Thanks, next'. As well as a notion of the Italic peoples being born loses through having become extinct, Irmion has also inculcated a strain in the view of historical development whereby roadblocks to Hellenic power and domination are roadblocks to Etruscan power and domination, and thus roadblocks to the evolution of his yet more advanced society still.
In its most generous incarnation Olikan philosophy not only tolerates but actively seeks to enhance the diversity of human society, to encourage the idea that humans are of one body through the notion that all spiritual traditions aim at universal truths, to respect and preserve indigenous culture whilst also promoting them across the world. But it is a spiritual tradition that was first propagated by Empire, specifically the Hellenic Koinon, and the connection of being non-Olikan and being non-Hellenic in the original usage of the term Ikthroy is not an accident; the Koinon always felt like Hellenic deities could substitute for, and subsume, most of the non-Greek pantheons they encountered, and non-compliance with their imperial domination was equated with rejection of the Olikan philosophy and vice versa. It's much easier to justify generosity of absorbing spiritual traditions of people you're not trying to conquer and, at times, subsume under your own cultural aegis. The use of Olikan principles to not only accord with Empire but actually to enhance and work alongside it is almost as old as the philosophy itself, and if a modern Olikan person/ruler/nation wants to justify a connection between their faith and the notion that some people need to be dominated for their own good they don't have to contort themselves into knots because that history is all already there. To these sorts of Olikans some things are too important to leave in the hands of the people that created them.
It's not hard to find cultural extinction a tragedy in cases where you think that society was mighty, powerful, and sophisticated, particularly where it fits a model that has been used to justify how and why your own society is now mighty, powerful, and sophisticated. Finding it tragic when you don't think of the culture in question as particularly potent, or connected to your own in any substantial way, that takes a different kind of perspective and empathy. That Kapotis, a sworn Phylakes of Apollo, found that within him is the reminder that whilst aligning with cultural chauvinism and imperialism comes easily to the Olikan faith it is by no means inevitable. Many of the ATL authors from 'recent' centuries with a similarly open mind towards both past and contemporary cultures in previous updates can be seen in that light also.