Eh.
Russian folk wisdom says "Жид крещёный - что вор прощеный. Веры нет" - "A converted Jew (slur) is like a forgiven thief - no faith/trust".
And in later times, "бить будут не по паспорту, а по морде" - you'll get beaten up on your face, not on (according to) your identification papers, a play on words meaning if you look Jewish, it doesn't matter that your papers say otherwise.
Your example of the Pale actually makes the point; Converting to Russian Orthodox actually released you from the rules imposed on Jews within the Pale. Conversion wouldn't save you from Nazis.