If there is one thing truthsharer is correct about it may very well be that the GRA was modern orthodox. HaRav Shimon Schwab zt’l said the chareidim are the real modern orthodox.
Selected Essays, pp. 90-91:
“And now we address ourselves to our chaveirim bedeah, our achim bemitzvos of the Orthodox Rabbinate of America. Ad masai? How long do you want to remain a branch, without becoming part of the tree? . . . We say to our achim b’mitzvos, “have Rachmonus with yourselves, and lemaan Hashem, part company with those who have given obscene semichah to to’evah clergymen” . . . Have rachmonus with yourselves, and break off your professional relationship with those who, for instance, consider Yishu HaNotzri merely a failed moshiach . . .We implore you . . . to part company with those gravediggers of Torah. I know it is a painful subject but it is unavoidable . . . We call on you to join us, the true Modern Orthodoxy , which is a generation of sincere mevakshei Hashem”.
Rav Schwab is referring to previous statements of his that MO is today outdated and “anything but modern”:
Selected Essays, p.89: