Something like that. I'm a polytheist/pantheist/animist, and a major part of my practice is paying respect to or celebrating various aspects of reality, whether they have tangible form (i.e., worship of sun or storms) or are more abstract/ideological (i.e., worship of learning or creativity).
But that aside, I still don't know of any theisms that are not supported in some fashion. People do not accept things without cause. There are reams of theological and philosophical arguments for classical monotheism, oodles of people who can testify to their personal experiences with various gods, strong familial and community bonds that underpin traditions, and so forth. I'm not limiting the notion of support and proofs to the narrow empirical or scientific sense, largely because I don't feel it makes any sense to do so in the context of areas like philosophy or religion. They're not science, and it makes about as much sense to me that philosophy and religion conform to scientific standards as it does to demand that creative writing and the fine arts conform to such standards. That's my general angle, anyway.
So circling this back around to burden of proof, maybe another reason it strikes me as silly is because I tend to view religion and philosophy as more like an art. If you walk into an art gallery, and someone says they think an abstract painting represents some particular thing, it should be good enough for them to explain why it resonated with them in that way. There is no authoritatively proving that the painting means X, Y, or Z. It's interpretation. And folks can have many different interpretations, discuss their reasons, and still disagree with each other. Sometimes I would like it if atheists defined themselves less in opposition to someone's interpretation of the painting and told us more about how
they see the painting. Perhaps from that angle, there is some truth in saying it is unfair to place any burden on them. But why place burdens on anyone? Not all theists are making authoritative truth claims when they speak of their gods - they're like the person in the art gallery saying "this is how I interpret this painting."
And now I'm probably rambling incoherently...