The Talmud, in tractate Shabbat,[2] quotes Johanan bar Nappaha who said one should wear the left shoe first.
Rav Kahana II also didn't care which shoe is worn first.
"[2] The precedence of the right in hand washing and using lotion were brought to Halakha by Avraham Gombiner and in the book Mishnah Berurah by Israel Meir Kagan.
[4] Avraham Gombiner, based on Isaac Luria books, added: "One should put both sides of the cloth on his right hand and wear the right side and then the left and have Kavanah that everything included in the idea of right and from the right comes to the left.
"[8] In the Israeli TV series A Touch Away, Roha'le Berman tells Zorik Mintz that pedantry in the order of wearing shoes is a way to test the potential spouse in matchmaking.