Consider a region where henotheism is widely adopted - i.e. tribes, families and individuals basically pick some God to worship, and stick with that, but believe in multiple gods. Greater life changes - conquests, natural disasters, interactions with new people - may mkae a tribe, a village, a family or a person decide to change gods. There is no formalized pantheon, but fuzzily overlapping zones with varying sets of gods recognized as even existing or relevant.
In this, a small tribe develops a religious view whereby they acknowledge the existence of Gods and various beings, but decide not to worship any of them; there is, however, a ritual life present.
The rituals include 'banishing' gods from former worship halls, in essence telling any God who attends a place that he is not going to receive any worship there for a while. This is renewed at intervals somewhat shorter than the religious festive cycles of neighbouring tribes.
When entertaining guests, an admonition not to thank nor praise any gods for the foods that are served is uttered. This admonition varies historically from not mandated, to mandated but freely worded, to a short 'anti-benediction'.