Is there an auto rigger for Rigify that also auto rigs the face?
I got all kinds of faces, I got foxes, horses, robots, googly eye aliens, etc.
Yes, of course, it’s even integrated with Rigify.
But make sure you use the “Human (meta rig)” and not the “Basic human (meta rig)” like in your image.
Last I checked using the “Human (meta rig)” gives you all the facial bones you need but doesn’t auto rig anything.
I don’t know of anything that will produce a Face rig for you…Perhaps Accu-Rig but I haven’t tried it yet…(an external Program for Character Creator)
Auto-Rig Pro has a semi-auto rigger… still need to place things by hand
This video might help you with rigging anthropomorphic animals…
But you are still going to have to do the alignment yourself.
If you do manage to find a software/app/A.I which can make a rigger’s job completely obsolete, please let me know! 
As I have been exploring Spline Skinning for Facial Rig in Blender —solutions that may be either Spline IK Bone Constraint or Bendy Bones— someone reinforced to me the quality of CloudRig Feature Set for Rigify Addon.
I never used it, and I’m not sure it possesses any preset Rigs for Faces (as Rigify Addon’s preset Meta-Rigs) that you might be looking for. But I already know CloudRig Feature Set indeed has got some Automation for Bendy Bones (probably as a Rig Type) which is pretty cool, although this also can be achieved with some older Addons that still work to this although with some bugs (such as Auto Bone Controller Addon).
For Spline Skinning on Facial Rig in Blender, I’ve also tried out another Features Set for Rigify Addon which is Experimental Rigs by Alexander Gavrilov. It has an Automation Rig Type for Spline IK Bone Constraint, which can be used for example to make tentacles.
The reason I mention Spline Skinning, is that, if we are relying mainly on Armature Deform (without Shape Keys), some highly expressive Deformations on Organic Rigging involving Stretch & Squash and very curvy shapes in motion, can hardly be achieved properly with the other Skinning algorithms Blender uses (Linear Blend Skinning, Dual Quaternion Skinning); this is why, even if Rigify Addon offers some Advanced preset Head/Facial Rig as a whole Sample or as part of some of its preset Meta-Rigs, this does not automatically implies it is Spline Skinning on its own, and so as I understand the Deformation results, coming only from Armature Deform in that case, might not be so thrilling for Facial Rigging.
main Rigify Extensions’ list in Blender Manual 3.4
https://docs.blender.org/manual/en/latest/addons/rigging/rigify/feature_sets.html
CloudRig in GitHub
These are generic notions… as I’d need more context to know what to recommend really.