Lisa Kron (who wrote the book and lyrics to the musical Fun Home) is trying to get at here, and I agree with it to some extent, but she has put it very badly.
Conflict -- which I think is what Kron means by "drama" here -- doesn't mean that the people involved aren't "like" each other. If anything it means the opposite: if they were that different, they might not come into conflict at all. Conflict often arises between people who are like each other: siblings, friends, etc. In one sense, all human beings are like each other anyway. One of the most harmful things people do is to try to defend their side in a conflict by Othering the person or people on the other side: in that falsehood is the germ of the most destructive human conflicts: You are not like me, therefore I can kill you. Therefore I must kill you.
Even stranger, Kron switches in midstream and puts the supposed unlikeness between the audience and the characters onstage, rather than between the characters in the play. It could be argued that one function of theater is to remind people that those they believe to be essentially different from themselves are really quite like them. I don't think that's the only function of theater -- or of any other medium of narrative, another objection I have to what Kron is saying: the function she ascribes to theater isn't unique to it. Theater, like any other art form (or any other human construction, probably) has no single function or purpose. Even if it had one in its first prehistoric forms, people have done many different things with it since then. And even if theater had a unique ability to bring the audience into a feeling of unity (though I imagine it shares that ability with any spectacle, e.g. sports), that unity will be against those outside whatever imagined community the experience creates.
This brings up issues of "universality," identification, and the like, which are involved in most art -- in the West, at least. I believe that what one gets from a narrative will depend very much on what they bring to it. If they are already predisposed to see the Other as like them, they will identify with the Other in the work; if not, they won't, and will find some other meaning in it.
I wouldn't be surprised if Kron contradicted herself about the function
of theatre on another occasion. Artists don't have to be consistent.
But it's generally a mistake to take too seriously what they say about
what they're doing. I once heard the recording of a panel discussion at a GLB writing conference, focusing on authors who write about characters "unlike" them -- a gay white American novelist writing about a straight Japanese student, for example. Some of the writers said that they loved getting "inside" people who were unlike themselves and letting the characters take over, etc. Then one of them said that he didn't get inside his characters at all, he gave them no agency, he decided what they were going to do and with whom. Immediately the other panelists reversed themselves and agreed that they did the same thing. I suspect that both descriptions of their approaches were true to some extent, though neither really was a fully adequate account.
I haven't yet seen Fun Home the musical, though I'm a great admirer of the Alison Bechdel graphic memoir it is based on. If Kron's statement in this meme reflects what she wanted the play to do, and believes it does do, then perhaps I shouldn't see it. Fun Home is much more complex than Kron's reduction would leave room for. From her many public remarks about the book, Bechdel herself is ambivalent about its relation to its readers. On some level she seems to have taken for granted that most people would not be able to see themselves in the story, and so was surprised by the rapturous response it won. She wasn't even sure she wanted straight readers to be able to relate to her queer narrator, I think. But to reduce Fun Home (the graphic novel) to an attempt to get its audience to "reach across that divide" does violence to its complexity and ambivalence. That's The Well of Loneliness you're talking about, Ms. Kron, not Fun Home.