A. The Code of Jewish Law advises against it, especially if it is flashy and bright. There may be a number of historical factors here (based on various Rabbinic texts): Red (back when clothing dyes were expensive) was considered to be a distinctive non-Jewish coloring at the time. Red also had some historical association with inappropriate behavior (think Scarlet Letter). And something about that bold, flashy and attracting ran against the spirit of Tzniyut (modest dress). Some studies suggest that red may be a more attractive color for men. Some say it was originally as response to anti-semitism, enacted so that Jewish women wouldn’t be flaunting, calling excessive attention to themselves, especially those women of means who could afford luxurious red clothing.

In terms of contemporary application, there’s some difference of opinion within the Orthodox community. Most ultra-Chassidish or Litvish religious communities would frown on red, some may ban it outright altogether.

Most regular Orthodox Jewish communities don’t have an issue with red nowadays, considering Rabbinic opinions that today clothing is generally more colorful, there’s less overall distinction between Jewish and non-Jewish dress (aside for some on Shabbos) and red doesn’t have the same distinctive association nowadays. Even for most people in Chabad the color red isn’t considered off limits. My daughters wear red if they like to, though it seems to be usually along with a different color.