Are the cabinet backs built as loadbearing components? Or is there a separate hanging rail dadoed into the sides? Framed or frameless? Brand? Different manufacturers have different construction and different best practices.

However, any screwed directly to the wall need the load distributed as widely as possible. That’s a GRK. Just be certain of the actual cabinet construction so that you are using the loadbearing construction element to attach. Screwing through a back that isn’t loadbearing would be very dangerous.

The screws also must go through the shims that are needed to get the cabinets level, plumb, and coplanar. If the shims are not done correctly, nothing is secure, or will stay level. That goes for the base cabinets as well as the wall ones. There are 6 dimensions to a box. Everything has to align in all 6 dimensions. Then be secured properly to each other and the wall so that they don’t shift.

The backs are load-bearing, and cabinets are frameless. I have read articles that coarse thread screws are best for melamine b/c of the material behavior. This made me wonder if GRK is appropriate given that if I understand correctly they are designed to engage wood.

If it's loadbearing, it should be 3/4" material, properly attached to bear weight. Pre drill it all. It's simple to do when you lay out the design and the stud locations. The point about the shims is important. Frameless are racked VERY easily by even professional installers that don't shim correctly, or that are not used to frameless. It's very easy to mess these up permanently and have wasted a bunch of your money.

Yes, the back is 3/4" thick (dadoed and grooved). So w/ predrilling, you think GRK are still fine?

Can I use GRK screws for building a cabinet with MDF board?

You don’t need cam lock hardware for MDF boxes. Cam locks are used on MDF cabinets to pull the cabinets together and most of the fastening strength is provided by dowels that are used in combination with the cam locks.

The right fastener really depends on the configuration of the boards and the load. Generally speaking thin shanks and big threads are best. However, if you are going through the sides and into top or bottom, practically any long screw will be fine. You should pre drill so you don’t split the MDF, but it should be doable. If this is a cabinet that might get racked, such as a small island, then pour a thin epoxy in the holes before screwing it.

There are plenty of great resources online for fastening MDF. Take some time looking for those.