As a result of this request (https://forum.inaturalist.org/t/default-map-satellite-view-in-personal-preferences/4146/12), the type of map view (satellite or map) is supposed to stick across the website. If you change the map view on one map, all successive maps you load should use that new map view until you change it again.
It looks like when you change the map view on the Explore page, it is not (no longer?) causing the map view in successively loaded maps to adopt the new map view.
Suppose, for example, you open 3 tabs. Tab 1 has the Explore page map, Tab 2 has an Observation detail page, and Tab 3 has a Taxon page with map. Suppose they all start with a Map type map view.
Change the map type in Tab 3 (Taxon) to Satellite, and refresh the other 2 tabs. You should see the other 2 tabs will now display a Satellite basemap.
Now change the map type in Tab 2 (Observation) back to Map, and refresh the other 2 tabs. You should see the other 2 tabs will now display a Map basemap.
Now change the map type in Tab 1 (Explore) to Satellite, and refresh the other 2 tabs. You should see the other 2 tabs are still displaying a Map basemap. If you refresh Tab 1, you’ll also see it goes back to a Map basemap.
Unless this is intentional, this behavior seems like a bug.