Below you can see a picture of a sandstone from the lower Buntsandstein group in Thuringia (Germany). The grey dots are sandstone, too. They are free of carbonates.
It's an interesting and probably difficult question. The rusty color of the sandstone will have a secondary origin during the oxidation of iron in the pore solution. There will probably be a link to the weathering. Depending on the color, it is most likely a goethite pigment. Unpainted round spots may have lower porosity. Some paleontologist may confirm that these may be fossil tracks. Perhaps corridors after raking worms. Maybe.
"Reduction spheroids are small-scale (diameter: few millimeters to maximum about 20 cm) spheroidal bleached features in red-bed sediments characterized by the absence of hematite and often containing a mineralized core (center, Figure 1). Reduction spheroids result from local chemical reduction of ferric iron and other elements. Host rocks are marine and continental red beds and, more rarely, altered, hematite-stained crystalline rocks. Reduction spheroids have been described from many occurrences in red beds of widely variable age worldwide..."
Most of these reduction textures can alter through diffusion processes into "cockade textures" or “fish eyes” with sulfides and selenides forming their nucleus. You find them in all red bed series in Central Europe, particularly in the Permo-Triassic red beds. In the Permian (plus Late Carboniferous ones) red beds and volcano-sedimentary series the nuclei are made up of sooty pitchblende and suitable for radiometric age dating. Organic matter not surprisingly is involved in this reduction and bleaching process. The coal petrographic data can tell you something of the diagenetic overprinting of the host strata as it is the isotope signature of the sulfides, selenides and the organic matter.
DILL, H. G. (1988) Sedimentpetrographie des Stockheimer Rotliegendbeckens - Nordostbayern (Bundesrepublik Deutschland). - Geologisches Jahrbuch, D 88: 3-67.(images therein)
DILL, H. G. (1987) Environmental and diagenetic analyses of Lower Permian epiclastic and pyroclastic fan deposits - Their role for coal formation and uranium metallogeny in the Stockheim Trough (F.R. Germany). - Sedimentary Geology, 52: 1-26.
DILL, H. G. and BOTZ, R. (1987) Mineralogy and geochemistry of carbonate mineralization and their role for environmental analyses of Lower Permian clastic and volcaniclastic sediments (Stockheim Trough, F.R. Germany). - Mineralogy and Petrology, 37: 251-266.
DILL, H. G. and BOTZ, R. (1989) Lithofacies variation and unconformities in the metalliferous rocks underlying the Permian Kupferschiefer of the Stockheim Basin/F.R. of Germany. - Economic Geology, 84: 1028-1046.
Some of them can be correlated with paleo-aquifers and paleosurfaces/ reaction surfaces so as to act as helpful tools for environment analysis
Can you please clarify by "They are free of carbonates.", do you mean A. sandstones as a whole are free from carbonates, or B. grey dots are free from carbonate and the red parts contain carbonate?