FWIW, I once heard a tape from Rabbi Rakefet (Nachum Segal show 9 days fare) where he said that Torah Umadda was supposed to be as opposed to Torah im derech eretz; TIDE believed that you could only be a complete Jew with secular knowledge, and the Rav held that they were separate.
Jews always dealt with the outside world. The gemara is full of references to Greek words, without being viewed as “modern”. The Slabodka bochurim dressed in the “conservative but elegant” clothing of their day, and did not view themselves as “modern”. Joseph here uses the internet and is a fan of HAM radio, and doesn’t view himself as “modern”. Unless you live completely in a shtetl, you deal with the outside world. Jews always did so throughout the Diaspora, without having to be labelled as modern.
So I propose we drop all labels except for “Shomer Shabbos” and “not Shomer Shabbos”.