This isn't a dependency graph problem..

The actual issue is caused by the following facts:

• Bevel is only allowed on pre-tessellated curve, while it is still guaranteed to have curve twist and other properties.
• Mesh sequence cache is a constructive modifier, which runs on post-tessellation state.

This makes it so bevel is never affected by the curve read from the cache. It *kind of* appeared to be working in 2.79 because mesh cache modifier was modifying object's splines, which is not only going against all designs we have :( but also was causing 1 frame delay during playback.

Now, with Copy-on-Write in place, cache modifier modifies copied version which gets tossed away after frame finished rendering.

The only proper and reliable solution i can think of here is to support real constructive modifiers for curves, which will operate on splines, and give splines back.

Maybe @Sybren A. Stüvel (sybren) will have time to look into proper solution one day. But for now unassigning from myself, since is unlikely i'll be handling this myself in the nearest future.