It depends on what you mean by that - it might mean “as a toolkit to create their own maps” (which is what it looks like AllTrails are doing above) or it might mean “just using an off the shelf MapBox style”, or it might be somewhere in between.
Here is a UK Ordnance Survey example that looks pretty close to Mapbox Outdoors, but is missing all of the vital access information that the AllTrails map has. That’s not a fault of the toolkit that MapBox provided, and might be an entirely appropriate style in some places in the world; the map that the OS present is their design choice and really doesn’t work in England and Wales.
At a stretch, you could argue that the OSMF are “using MapBox” by creating vector tiles in a Mapbox-compatible format 
.