"Because maybe people outside the norm, like gay and trans people, people of color, would like to see themselves reflected within the classics American theatre?"
But plays aren't written to include or not include splinter groups. It's forcing a perspective on a work that doesn't belong there. If the gay community wants to celebrate Shakespeare for writing cross-dressing into his plays, then that is fine, but it shouldn't be shoe-horned into a piece.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.