(Crossposted to whatwasthatbook.)

I seem to recall that said author was a woman, and the series as fairly recent/ongoing. The Species Hat of these mice was a compulsion to imprint religiously--the way that ducklings will imprint filially upon the first living creature they see--on whatever might happen to awe them; I recall objects of worship including a cake, an oak tree, and a chicken (I imagine the last was a short-lived denomination, to judge by various YouTube farming videos.)

The most fortunate bunch chose the protagonist and her family--who were prepared to deal with and protect eccentric sapient critters--as their pantheon.

ETA: nocowardsoul has identified the source as Seanan McGuire's InCryptid series.