I'm renovating my kitchen. The current cabinets were screwed into 2x2s and in some cases directly into a cinder block wall. I'm not a fan - it makes it difficult to run my electrical. However, framing the wall with 2x4s will push the wall out just enough where it makes the refrigerator opening awkward. Not impossible, just close enough to a window where opening the refrigerator would be awkward.
Any issue (other than code requiring 2x4s?) with using 2x3s to frame the wall? It is not load bearing (for the house; obviously it will bear the load of the cabinets plus contents). The 1" saved on the depth of the wall will really help. To be clear, I'm not exactly sure how much it will save me as I haven't demo'd the existing kitchen yet to confirm the exact size of the lumber currently used; I'm basing it off of what I can barely see through a hole under my sink. but I know it is not 2x4s.
Regardless, if 2x3s are just fine it will save me some space. I plan on using blocking between the studs to make hanging the cabinets easier.