With regard in particular to the basic dress of your average frum Torah Jew, e.g. white shirt and black trousers, this is not necessarily ‘old’. It is a relatively common modern style. What marks it out is it’s formality, and it’s uniformity. Or in other words, that we all wear it, all the time (I’ve focused on men for simplicity).
The two primary reason, amongst others, for this mode of dress are relatively simple. Dignity and identity. Firstly, dignity. If you consider the alternatives, the most common casual modes of dress amongst the general population, i.e. jeans, t-shirts, etc., apart from often being immodest, simply do not convey the dignity apropos of a Torah Jew. By dressing in a formal and relatively distinguished manner, we are conveying a desire to dress in a manner fitting to the way we aspire to lead our lives.
And identity too is important. The ‘yellow star’ analogy is offensive and misguided. Maintaining a strong distinct identity is important, indeed crucial, to the effective observance of Judaism. Other cultures dress differently for precisely this reason, and feel no need to apologise or self-flagellate for doing so. And when what is being preserved is a not simply a cultural identity, but a religious one, it gains extra levels of significance and importance.
I would like to add that nothing of what I’ve said above means less homogeneous dress, whilst maintaining dignity and a Jewish identity, is invalid or wrong. Simply that this is a correct and important practice, and should be recognised as such.
And on a personal note, when I travel or simply go out, being dressed in this way, clearly Jewish, dressed more formally, and in a far more dignified manner than most around me, certainly enhances my connection to yiddishkeit and my inherent value as a Jew. To paraphrase Shakespeare and/or Mark Twain,
“Clothes make the man”