Heshy,
I think there’s more to your question than an academic “should they wear this”? You might need to sort out some personal questions as to why this irks you. If you are worried about “what will the Nochrim say”, you would have left home without your yalmukah. So it is not the “Jewish dress” per se, but the type of dress that stirs something in you, and makes you feel uncomfortable in some way. Think about it.
When you feel completely comfortable in your own skin, and completely serene in your own choice of dress, you will no longer feel irked by the choices of others.