Occasionally I will post questions that have been asked on my Curious Cat page (where you can ask me all kinds of questions anonymously). These will be exactly as they appear on the Curious Cat page, but I may expand on my answers slightly in separate posts, or below the original answer.
Where do you think the field of Greek religon is moving after polis religion?
This is a very loaded question, and you will get as many different answers as scholars of ancient Greek religion.
The first thing to say is there are a lot of good things about the polis religion model, and it has helped us over the last 25 years advance the study of Greek religion immensely. It has become, and I think will continue to be, a starting point for new scholars of Greek religion - certainly until there is a new model as widely accepted and used as polis-religion.
To my mind, polis religion has two major flaws: it doesn't account for 'marginal' personal religious practices (this has been really well-explored by scholars like Esther Eidinow and Julia Kindt), and it doesn't account for personal religious experiences: the simple fact that people are different, experience things differently, think about things, believe things all differently.
That's why I think the future of the field (and my own work) will lay in materialism as a theoretical framework (in fact, I am planning to write an article about this very thing, and how it can be used in ancient history!).
Materialism is closely linked to sensory studies, but not quite the same (though they are highly complementary!). It can allow us to conduct ethnographic studies through 'lived' experience, objects, practices, traditions, and spaces in a place where we cannot conduct direct ethnography. When applied to the study of religion, this means that we look at how people encounter in their ‘everyday world’, as well as the sensations and feelings of everyday life, focused through the lens of religious practice. It can be focused through other lenses, and even in the study of religion, it's important to take civic, political, social, and economic lenses into account (this is another question, about religious embeddedness!).
I want to be very clear that this is not THE way forward. The future of the study of Greek religion will be, I think, a patchwork of interweaving and overlapping methodological and theoretical frameworks for which my part will, I hope, be the introduction of Materialism. There is already wonderful work being done in and through sensory studies and cognitive approaches (Jenifer Larson's recent Understanding Greek Religion is an excellent introduction to this).
And, I think that it will be quite a while before we can move on from polis religion and the influence of Christiane Sourvinou-Inwood.