From Lin-Manuel Miranda’s "Hamilton" to Denzel Washington playing an Irish American in "The Iceman Cometh" - finally we're moving on and having these conversations.

If there is any doubt about who the most dominant figure in American drama is, take a look at New York’s theater scene right now. One hundred and thirty years after his birth -- and 65 years after his death -- not one, but two of Eugene O’Neill’s great works are being staged.

Each is well over three hours long.  Neither has a single song or talking animal in it.  Yet they are playing to packed houses, and feature Hollywood heavyweights in starring roles.

First, there’s A Long Day’s Journey Into Night over at the Brooklyn Academy of Music, starring Jeremy Irons.  The play is an epic exploration of the haunted Irish American Tyrone clan.

Then, over at Manhattan’s Bernard B. Jacobs Theatre, there’s Oscar winner Denzel Washington alongside Irish actor Colm Meaney in The Iceman Cometh.  If A Long Day’s Journey is a study is claustrophobia to the point of stifling oppression, Iceman is a raucous night out at the bar with pals, whose laughter and smiles are masks to cover all manner of human weakness and suffering.

The O’Neill plays -- and their various Irish and Irish American characters -- come to us at a very interesting time.  On the one hand, thanks to Lin-Manuel Miranda’s groundbreaking Hamilton, there is a new wave of fluidity in casting and storytelling.  In that spirit, Washington has assumed the starring role in Iceman as Hickey.

Though written as, and traditionally played by, white actors (including Irish American Nathan Lane in a revival a few years back), Washington has not only earned raves as Hickey, but the cross-racial nature of his casting has more or less gone unmentioned.

But there is another movement out there, one that is moving things in the opposite direction.

Consider the long-simmering controversy over the hit animated TV series The Simpsons, and the accent of Kwik-E-Mart store owner Apu.  For decades, Apu was voiced by actor Hank Azaria, and Apu’s thick accent was considered part of the humor.

But a few months back, a documentary entitled The Problem With Apu came out, which argued that Apu’s accent has given some folks the idea to mock or bully Indian or other south Asian immigrants.  Azaria has even publicly stated that he would be willing to stop providing the voice for Apu.

This is only the most recent debate revolving around who does and does not have the right to tell certain kinds of stories.  HBO got into hot water last year when it announced two white Game of Thrones writers were developing a series set in an America where African American slavery still existed.

Then there is young adult author Keira Drake.  She was briefly the toast of the literary world when buzz was building for her first book The Continent.  That is, until early readers took to Twitter blasting Drake’s “troubling portrayals...of people of color and native backgrounds,” as one petition put it.  (Drake eventually took the extraordinary step of rewriting the entire book.)

The Irish do not fall easily on either side of this debate.  On the one had, it does seem a little, um, weird to have such a thoroughly British actor like Jeremy Irons portraying immigrant James Tyrone who, for all of his fame and fortune, is haunted by the poverty of his Irish Famine-scarred youth.

And while there was once a time (not long ago) that not mentioning Washington’s race in Iceman would be seen as progress, one can now ask whether or not it is realistic a bunch of white drunks in 1912 would really be pals with a black guy.

Meanwhile, looking ahead, should Italian American Robert De Niro really be portraying the title character, Frank Sheeran, in Martin Scorsese’s forthcoming epic The Irishman?

It will take some time to sort all of this out.  But since we are discussing these things, can we at least make sure that actors never again mangle either the Irish accent, or the “Noo Yawk” accent so often attributed to Irish American wise guys?

That alone would make the world a better place.

Read more: Nine Irish-born leaders who made a difference in America named

Denzel Washington in the Iceman Cometh.