I can't tell how finished and "proper" you need this. Obviously, fiber cement siding isn't designed to take the weight of cabinets, so the premium solution would be to take it off and cut it out wherever you want to hang them. It's not doing anything for the envelope other than acting as a rain barrier and under a porch that should not be a concern. (If it is, I'd be more worried about how are the cabinets going to hold up!)
I'd patch the screening so it keeps out the bugs to avoid concerns with any insect haven. Then scribe the blocking as others have mentioned. Don't seal, just let it breath.
The simplest solution would be to make French cleats, top and bottom, mounted on 2x4 blocking via long 1/4" wood screws through to the studs and painted to match the siding. Hang the cabinets on these. Don't worry about the air space behind the cabinets. Or put screening around the gap.
How many cabinets? Those mudroom seats with wall cabinets/cubbies above as stand-alone furniture are popular. For just 36-60" of wall cabinets, you could make a large bench with a back that supports the cabinets so it is all movable.