pH - through protonation - changes concentration of the ion needed for ppt.
Oxalic acid is a weak one (pkA1 = 1.25, pKa2 = 4.27). For 0.1M oxalic acid solution at pH = 8.6 oxalic acid is dissociated 100%. In the same solution with pH = 1.3 only about 0.1% of oxalic acid is in form of Ox(2-), the rest is about 50/50 split between HOx- and H2Ox. This gives 1000 times difference so the solubility of oxalates will change 1000 times between pH 1.3 and 8.6.
Ox stands for C2O4.