ZD – it was an American Bais Yaakov girl.
Even in Israel, no one has a problem with girls learning english (I don’t know about Shakespeare though). All the Bais Yaakovs teach english (or at least almost all – there could be an exception, but I haven’t heard of any)
The boys don’t learn english in school, but many learn out of school, and I have never heard of anyone objecting. I even have a friend whose son is in a Yiddish school, and he gets english lessons. She wouldn’t do it if it were against the rules or considered OTD (and yes, the kids are trilingual).
The issue that R’ Chaim had with shakespeare was not that it’s english. I believe the issue was that the RY who asked him said that it has the 3 aveiros chamuros in it (although I am a bit reluctant to quote something that I heard third-hand several years ago, and can’t guarantee 100% accuracy). But the issue was definitely not that it’s english.