Read the appliance specs of thevovens you are considering. But if its a face frame cabinet, the face frame is all the support strength of the cabinet. Standard face frame width is 1 1/2”. You do not want to cut that down to less than 1” in a big tall cabinet like that, even if the internal dimensions are roomy enough for the specs. It all starts and ends with the appliance specs.

These are not face frame cabinets. I think they are referred to as European style. There are vertical 3/4" panels that form the sides of the cabinets and the doors hinges are set into mortised round holes in the side panels. I've looked at the installation instructions for various oven makers units and can't see anything specific about minimum spacing between the oven and the side wall of the cabinet. I think there might be enough meat in the front panel of the cabinet to open the width up enough to accommodate the 28-1/2" that most 30" ovens call for. But this would only give me less than 1" of clearance (on each side) inside the cabinet depending on the actual width of the inserted part of the oven. It looks like the inside width of the cabinet is about 29-5/8".

"I've looked at the installation instructions for various oven makers units and can't see anything specific about minimum spacing between the oven and the side wall of the cabinet."

Yes, required spacing is around the cutout, not between the oven and the cabinet interior. For example, the Installation Guideof the LG LWC3063STrequires least 1" on all sides of the cutout. The Dimensions Guideof the Maytag MMW9730FZrequires 1" only above and below the cutout. Both assume the exterior width of the cabinet is 30" and that the cabinet can handle the oven weight and withstand high temperature.

-- amateur