Back when I was first getting started with polytheism, I tried to build some affinity with the deities of the Irish pantheon, as I know I have some ancestral heritage there. As much as some of the gods appealed to me though, I didn't seem to appeal to them, and I never felt much responsiveness.
At Yule 2011 at CedarLight, we honored some of the Norse gods, and they seemed to be very "present." For quite a while after that, I made regular offerings to Odin/Woden at home, and read up on both Asatru and Anglo-Saxon Heathenry.
This Spring, though, the Greek gods caught my attention, Hermes in particular, and after a couple of dramatic answers to requests, I began to call him my patron god. The Hellenic culture appeals to me intellectually, as much of their original pre-Christian mythology and philosophy has survived through the centuries.
But then the weather turned cooler and it was as if Odin returned from travels and knocked on my window again, much like Gandalf, and now the deities and culture of the northlands are again top of mind.
All of this fluctuation, coupled with some of my initial study on ADF's clergy preliminary program, has led me to the conviction that ADF's notion of "hearth culture" should be only a starting point. In the reality of history, the cultures of Europe mingled and mixed and migrated, and gods were worshiped far from the lands where they originally appeared.
I've been thinking that perhaps there is some value in a pan-Indo-European hearth. In practice, most of the ADF members I know do not limit themselves to a single hearth culture, but choose – or are chosen by – those deities that they find affinity for. Nothing in ADF discourages this, but the hearth culture paradigm as presented in the Dedicant Manual might leave the impression that our ancestors lived in isolated bubbles, either Norse or Roman or Gaulish for example, when the reality was much more dynamic.
So, to extrapolate from history, the various IE cultures encountered each other and shared their ideas and religion fairly broadly until conversion eventually overtook the land. Had that not happened, it stands to reason that the process would have continued to the point that rather than a set of distinct pantheons, the gods of all the lands would be known more universally and available to all. While it seems likely that a Norseman would still be more inclined to make offerings to Thor or Freyr than to Ares or Lugh, a person with a mixed ancestry – as is true of most 21st Century Americans – might not have the same strong ties.
What I am thinking toward, and the work is far from done, is to simply articulate in theory what is already frequently the case in practice. I will post more as my thinking develops.