You make a good point on the question of what I mean by religion. I would say, I want to avoid the dogmatism associated with mainstream institutionalized religions. Something like what I assume you mean by "fixed ontology". Weil, on the other hand, argues that we should embrace it and argues that there is value/beauty in the ceremony, rituals and rites offered by churches.
She really occupies an interesting space. Her contemporaries were the likes of Sartre and Simone de Beauvoir. I think that secular humanist crowd was totally unwilling to entertain mysticism. Also, Marx was ardently against religion seeing it as a tool of oppression. So Weil was unique in that she was aligned with them on political and economic issues, she was a grass-roots labour activist to the core, but she was also deeply spiritual and mystically inclined. Her criticisms of Marxism are heavily inspired by her belief in a transcendent divine that is completely absent from normal leftist/materialist view points.
It is sad that she died so young, at 34, before she could more deeply explore this political philosophy. It is interesting to consider what kind of political ideology you might get if you take the core understandings of Marx and even the post-modernists but you re-inject a non-dogmatic mysticism.
I have had a similar journey in the last years, drawing more and more inspiration from Christian, jewish and muslim contemplatives, after years of mostly following a "secular Buddhist" path (basically buddhism without believing in rebirth. Which becomes quite thin, as buddhism is the path towards the end of rebirth...). I am not sure of what you mean by "religion", but what I am convinced about is that we need to allow for more "religiosity" than what the typical mindfulness/secular Buddhist movement allows. What often happens (or happened, as I do not pretend to be an innovator there) in those circles is that the rejection of religiosity means that a lot of assumptions underlying our culture (mostly the materialist ontology) goes unquestioned. There is actually lots of values in opening to religious interpretations of mystical experiences, and opening the range of possible interpretation. Without falling into a new fixed ontology, therr is something freeing in allowing oneself to think in terms of "the divine", "the ground of soul" or "the eternal present".