https://forum.inaturalist.org/t/option-to-use-openstreetmap-in-the-app/59445/3
It’s possible this option will get added in the future. Right now the risk is running in to limitations on the tile usage of OpenStreetMap directly from the servers of the OSM foundation.
Since the servers are payed from donations they have a limitation of tile usage. If a project like iNaturalist will make too many request it might get blocked to keep the service affordable and possible.
Right now iNaturalist is getting Google maps tiles for free without limitations. INaturalist would probably need a similar agreement with one of the big providers like Mapbox or MapTiler to be able to default to OSM (or make the option to use OSM background more widely available)