I’ve noticed a couple of different routing engines being affected by cattle grids along the route. Sometimes they’re just not something that the engine will route over.
Is there tagging that should be included with cattle grids that helps with routing? IE, motor_vehicle=yes or something like that?
What affect would access=yes have?
I’ve experience this with OSMAND and also on a website RideWithGPS.com.
Is this a problem with routing engines or a lack of tags?
I think it is a problem with the routing engines and you should file a bug report with them.
But to be fair, OSM tagging is a bit of a mess and the fact that most but not all barrier=* values imply you cannot proceed further can be confusing to mappers and data consumers alike.
It is possible that a access=yes would help the routers in question. So even though it might be construed as “tagging for the renderer” you could try adding that tag.
And I’ll make a mental note about that next time I tag a cattle guard (as they are called where I grew up).