The Kollel wrote on Avodah Zarah 29-
>> The BI'UR HA'GRA questions the view of the Ran. The Yerushalmi says that a person is not allowed to use a mirror on Shabbos for fear that he might pluck out a hair (a forbidden act on Shabbos). It then says that a man is forbidden from using a mirror even during the week. The Bi'ur ha'Gra asks that it does not make sense that the Yerushalmi is saying that the custom is that men do not look in mirrors during the week, because the Yerushalmi says that it is forbidden , implying a strict prohibition. The Bi'ur ha'Gra therefore sides with the Shulchan Aruch. However, REBBI AKIVA EIGER (YD 182:6) in the name of the GINAS VERADIM, and the GILYON MAHARSHA in the name of the MAHARI MINTZ, rule like the Ran, which seems to be the way most Poskim rule. (See YECHAVEH DA'AS 6:49, who rules leniently even for Sefardim and Talmidei Chachamim.) (Y. Montrose)<<
You did not mention the responsa of Reb Moshe Feinstein, zt'l on using mirrors in Yoreh Deah ll:61. He says they are totally prohibited today.
M. Kaplan, Yerushalayim
While it would have been worthwhile to mention the Igros Moshe, the custom to be lenient is still solidly based on the Rema (Y.D. 156:2) in the name of the Ran (and other Rishonim), who permit a man to look at himself in a mirror. (The Igros Moshe clearly states at the beginning of the Teshuvah that his explanation is based on the Gra - which is quite obvious.)
All the best,
Yaakov Montrose