This track just caught my attention: Way: 26457459 | OpenStreetMap
It is (imo superfluously) given access=agricultural, foot=yes, bicycle=yes, and carto renders it as a slightly greyed-out red dotted line (like access=no or private, unlike tracks without access tags, which are brown).
Is that a new way of rendering? I don’t remember seeing it represented this way.
The very general
access=agricultural
seems to be a relic from the olden days which marks this way as needing survey to check if there’s a VZ250 or VZ260 or maybe something different.
As far as I can see there gave been some slight changes in rendering of ways and that’s a good thing in my mind. Carto isn’t just any mapstyle, it’s our immediate feedback mapstyle so this actually helps discorvering ways with this old, rather restrictive, tagging.
(I know that there’s overpass to find these ways. Still, a way to see it on The Map™ is nice)
It’s a forest track, which is restricted to agricultural and forestry traffic and allowed for cyclists and pedestrians. So while I personally find it superfluous, I feel it would be wrong to remove the access tag, cf. wiki. On the other hand, the greyed-out red seems to suggest that the track is closed even to cyclists and pedestrians. I wouldn’t know what to do here.
This rendering is about 10 month old, so not really new 
See
Thanks, that was helpful. So the point is that agricultural is now interpreted as no. Hm. That makes sense if you drive a motor vehicle, but not if you cycle.
It is not possible to render different access for all types of vehicle at the same time.
access=agricultural within a forest is wrong. typically only vehicle are restricted (perhaps (motor_)vehicle=agricultural;forestry (+ bicycle=yes))
Maybe this is the relevant (13 year old) sign?
OpenStreetMap Node: 1847758664 | OpenStreetMap
But doesn’t fit to this photo Mapillary from 2019 (this looks more like (vehicle=forestry or vehicle=agricultural;forestry)
As @Langlaeufer pointed out: traffic is different from vehicle.
Most German forests can’t restrict bicycles so it’s important to know exactly what kind of sign we’re dealing with and possibly what the Waldgesetz of the state in question says.
Generally speaking: Most forrest highways in DE are motor_vehicle=forestry but it usually needs survey.
Yes, of course I agree that that isn’t possible. What I found strange is that it is greyed-out red rather than greyed-out brown so I believed there might be a mistake in the rendering. Or that the idea was to render track closed to general vehicles as a path.
But yes, access is wrong, I didn’t think of that. Replacing it with motor_vehicle is probably the answer.
It is not possible to render different access for all types of vehicle at the same time.
rather it would be possible but it is not desirable and would likely be very complicated and confusing. 
In addition, vehicle=* is a relatively late addition as a traffic mode (being approved in 2008 when OSM was founded in 2004 and its access was tagged around the time it got approved) and the standard before that was to use access=* which includes pedestrian (definitively not vehicles) and equestrian (who may or may not count as vehicles) access, hence the need of adding exceptions to the list.
(thinking of access, surface and surface smoothness in Osmand?)
The assignment of words to colours are weird. Orange is a yellowy shade of red (YMMV), having noticeably more red than green (yellow being red and green) and brown (which is dark orange) veers even further towards red than yellow to the point where you can describe some dark red colours, particularly with less saturation, as brown (case in point: CSS has defined maroon as “#800000” i.e. without any amount green to make it slightly yellowish).
In fact, checking the colours reveals is that the track has near exact values of red and green (albeit at very unsaturated colours so the difference is still huge, relatively speaking) and so can be simply thought of as the original track colour, just with less saturation.
The other reason is that the eyes play tricks on you and the track will appear more reddish to stand out from the green of the forest.
Yes, this is particularly difficult for highway=track (open issue here), and so only the simple access tag is considered to decide on the rendering. access=agricultural (along with forestry) is now treated as access=private.
The “private” rendering of tracks is a bit ugly / hard to read though.