Definition of OTD and “modern” is very challenging.
It a father where’s a long coat on Shabbos and opposes Zionism, and the son wears a modern suit and supports the medinah, is the kid OTD? If someone who follows any aspect of Shabbos (e.g. not going to work, but otherwise doing all 39 melachos) or kashrus (not eating treff animals, but otherwise ignoring kashrus), still considered OTD?
Is some considered “modern” only if they are a zionist who learns Torah some times, but wears American-style clothes and follows liberal/zionist rabbanim. Some people would say the someone who belongs to a nominally Orthodox (meaning frumer than Conservative) shul but almost never attends, and makes makes no attempt to keep kosher or Shabbos, is still “modern” and that to be OTD you need to completely give up on Shabbos and Kashrus.