One of my players is about to buy an anthroform drone and plug-in a Response 6 she built and a Pilot 6 she programmed herself instead of a brain in a jar.
She's probably going to do some customization before the thing gets up and running but, after that, I get the sense that she may want to add on a cyber-arm or two to boost it's combat capabilities.

So, would you allow a anthroform drone to be outfitted with cyberware? Why or why not? Thank you.

There is already a system for upgrading drones. Cyberware is not optimal, as it contains interfaces with biological systems that don't exist, and no interface really for vehicles.

Vehicle mods, only, in my game.

Yes, using the Full Mechanical Arm = Cyberlimb rules.

However, its far from complete, and there are instances in which houseruling is necessary, or some pieces of equipment don't have Capacity listed.
one such instance from our table would have been our techno rigger putting cyberskates on one of their anthroform drones. There was a mod slot left unfilled, so it was given the OK.

Things to keep in mind:
This is what special machinery is for.(arsenal mod)
Forcing people to use overmodding to represent the increased cost and technical difficulty in doing exotic or wierd installations is not necessarily a bad thing.
Full Mecharm->cyberlimb capacity is a decent start, and can be extrapolated to, say, use cyberleg mods if someone so desires.
Examine what the player wants to do, then go from there. This is the important bit: Figure out what they want to do specifically, then go from there.
Realize that the rules system is limited, and that essence-built full limb "cyborgs" will probably have more toys than a vehicle-based 'cyborg'. Dont be afraid to explore the middle ground, and work around the system. A good example of this is Cameras vs Sensors. Cybereyes are just so much better, and it doesn't make sense.

In your case, what I would suggest is extrapolating a Full mecharm/Cyberlimb cost-benefit, and turning it into a "Modification Slot for X Essence of generic cybermods" deal. I am unsure what a good balance ratio IS, but try 1:1. I was going to suggest a 1:1.5, so that a 'cyborg' drone using all its modslots for ware would have as much potential as an essence 6 metahuman, but that is kind if nitpickey.
Go for it. Let the player go nuts. An encouraged player is a productive, contributing player - the best thing you can do is look at what she wants to do on a case by case basis, and go from there. There IS framework within the rules for this kind of situation, but its pretty much all gm discretion.

That.

Same here. No need to go with Cyber at all.

i only accept cyberlimb mods that don't exist as a vehicle mod and don't change vehicle stats.
and only if the anthromorph is metahuman sized. No cyberlimb mod for your bust-a-move.

so i allow : Cyberarm Slide, Cyber Holster, Hydraulic Jacks, Scanner System, Snake Fingers, Telescoping Cyberlimb, and Modular Plug-In.