Q. I heard from a chasidisher fellow that even if you answer daily to a “gut morgen” greeting in Yidish, a “gut yohr,” as many do, on New Year’s day you should avoid saying it, because of the connotation of the goyishe year. What is Horav Miller’s opinion?

A. Horav Shlomo Miller’s Shlit’a opinion was recorded on question 695, namely: If someone greets me with a “Happy new year” can I respond likewise?
A. Horav Shlomo Miller’s Shlit”a opinion is that it is permitted since in our days there is no religious connotation to the greeting. In addition, you may initiate the salute if it generates a Kidush Hashem by displaying good manners.
Ohalei Yakov (p. 20) quotes in the name the Apter Rov Zt”l, the meaning of the Posuk (Tehilim 87:6) “Hashem counts in the script of the nations” as conveying that during their New Year we are also granted retroactively a better Rosh Hashono judgment. Since the differences between the individual conduct during the two celebrations, becomes now widely apparent and evident, therefore a Good Year salute to anyone is not out of place. (Nitey Gavriel ”“ Chanuka p.418).
Sefer Chasidim (51) quotes the tradition of one doubling the blessing given, when responding to a greeting. Talmud (Gittin 62a) rules that we do not double a sholom greeting to an Akum and therefore Rav Chisda would greet them first, (as the Ran explains) to avoid doubling the greeting. (See Alei Tomor p. 229, 274)
Horav Shlomo Miller’s Shlit’a mentioned that this applies today when greeting a Gentile.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a.