I don’t doubt there are Modern Orthodox shuls where most women cover their hair. What people have to remember is that there are a ton of Modern Orthodox shuls all over the country (not just in the areas with good communities like NY, NJ) where they are the only Orthodox shul in town. In these places, tznius is totally off the radar. When the only other Jews in town are reform, all you have to do is not wear short-shorts to be “super machmir” on tznius.
On my “before it was cool” comment. What I mean is that I was criticizing her geirus before everyone on the internet was.
Picture this hypothetical: you’re a serious convert, and you find that the beis din you’re using converted the daughter of a high profile figure who is now going around publicly speaking in sleeveless shirts and uncovered hair. You want to change to another beis din, but you can’t because the Zionists have pigeon holed all conversions to go through the left-wing RCA.
I heard a rumor (probably more likely than the OP’s rumor) that Ivanka didn’t actually go through a Rabbanut recognized beis din. Not sure if that’s true.