Interesting! I don’t use OSMAnd, so I didn’t know that.
I’ve just checked the three routers on openstreetmap.org with some example locations.
Looks like GraphHopper and OSRM will route cars and bicycles through an untagged gate (see
here and here). Valhalla prefers a longer route to the same destination, avoiding the gate. All three routers will route pedestrians through the gate.
When there is no other way to get to the destination e.g. here and here, all three routers will route through the gate.
If I am reading the documentation right, Valhalla will take a detour of up to five minutes to avoid a gate without access tagging. The other two routers seem to ignore it, at least in their default profiles.
Organic Maps behaves similarly to Valhalla for cars but routes cyclists through the gate.
I tested this in Scotland and Thailand. I don’t know if the routers use any country-specific defaults.
Not sure what to conclude from this. When I know who is allowed through, I tag it, when I don’t, I don’t 