In this work, we have developed a method for the preparation of pH-responsive track-etched membranes (TeMs) based on poly(ethylene terephthalate) (PET) with pore diameters of 2.0 ± 0.1 μm of cylindrical shape by RAFT block copolymerization of styrene (ST) and 4-vinylpyridine (4-VP) to be used in the separation of water–oil emulsions. The influence of the monomer concentration (1–4 vol%), the molar ratio of RAFT agent: initiator (1:2–1:100) and the grafting time (30–120 min) on the contact angle (CA) was studied. The optimal conditions for ST and 4-VP grafting were found. The obtained membranes showed pH-responsive properties: at pH 7–9, the membrane was hydrophobic with a CA of 95°; at pH 2, the CA decreased to 52°, which was due to the protonated grafted layer of poly-4-vinylpyridine (P4VP), which had an isoelectric point of pI = 3.2. The obtained membranes with controlled hydrophobic-hydrophilic properties were tested by separating the direct and reverse “oil–water” emulsions. The stability of the hydrophobic membrane was studied for 8 cycles. The degree of purification was in the range of 95–100%.