The offensive practice of actors donning “blackface” or “yellowface” is largely retired. Next to go may be what some call “cripface.”

Carey Cox plays Laura in “The Glass Menagerie,” which opens Friday at the Guthrie Theater. Cox believes that Laura, a rare classic character who is written as disabled, should be played only by disabled actors. (Cox, who uses a cane as a result of a joint-weakening disorder called Ehlers-Danlos syndrome, describes herself that way; others prefer “actors with disabilities.”) The drama features a writer who recalls what led to his parting from his mother and sister, Laura, who walks with a limp.

Cox says “cripface” (or “cripping up,” which she prefers) describes able-bodied performers who play disabled characters. She cites many reasons Laura should be represented by disabled actors.

“She says, ‘Mother, I’m crippled.’ That comes up a couple times. She talks about wearing a brace on her leg and clomping up the stairs. It’s actually written into the stage directions,” Cox said. “With someone who is not within the disability world, that’s where Laura becomes a stereotype or the acting becomes all about her disability. It’s a reductive way of looking at her.”

There’s room for disagreement about casting Laura.

Regan Linton, who uses a wheelchair and played Laura in college (and was in Mixed Blood’s “The Curious Incident of the Dog in the Night-Time”), believes Laura should at least be played by an actor deeply familiar with the disability community. Joseph Haj, director of the Guthrie’s “Glass Menagerie,” wanted an actor with a disability but knew he also needed a “gigantic talent.” Mixed Blood artistic director Jack Reuler, who affirmed his company’s commitment to telling stories with artists who have disabilities two decades ago, wonders if the 2017 Broadway “Glass Menagerie” changed how future Lauras will be chosen.

“Before Paul Robeson played Othello, there had never been anybody black who played it on Broadway. But, after Robeson did it, it’s rare that anybody would think of the role in a different way. Maybe that’s what that ‘Glass Menagerie’ did for American theater,” said Reuler of a production that opened with its Laura — Madison Ferris, who uses a wheelchair — dragging it up a flight of stairs onto the stage. (Cox was Ferris’ understudy. Onstage, she also used the chair, although she does not generally use one offstage.)

All agree that using a wheelchair is one thing to consider when auditioning actors, along with whether they can sing or have brown hair.

“It’s too simple to say you cast someone because of one aspect of identity. That’s a piece of the overall package any actor is bringing,” said Linton, who also is artistic director of Denver’s Phamaly Theatre Company, founded by artists with disabilities.

Haj said Cox’s overall package won her the role. She spent a few years in the acting company at his previous gig, PlayMakers Repertory Company.

“Carey has a kind of transparency. You read her thoughts. It’s a rare, rare actor’s gift,” Haj said. He brings to “Glass Menagerie” his experience of growing up with a father whose blindness bumped up against “a world that can be decidedly and sometimes aggressively unaccommodating.”

What it feels like to be fragile

Cox doesn’t have to research or imagine many aspects of Laura. “I had a lot of trouble in grad school with the way I hold myself. It’s very protective, very physically protective, because I don’t want my bones to dislocate. That translates to an emotional protection, too,” said Cox, who sees that as a key tool for depicting Laura. “I actually feel more connected to my body as a storyteller than I ever did before because I understand what it feels like to feel fragile.”

Cox’s cane is crucial to this “Glass Menagerie” because how she moves through the world is part of the story.

“I’m using it as an acting choice: when we use the cane and when we don’t. It kind of tells a story because when I use a mobility aid, it does make me walk in a more ‘normal’ way, but you notice the mobility aid. When I put it down, you don’t see it right away, but you can tell the difference in the way I walk. I can’t escape it. It’s so much a part of me,” said Cox, adding that when Laura uses her cane will reveal how comfortable she feels.

Which is true of Cox, too.

“I have that question every time I walk into an audition room because the cane is an obvious signifier of disability,” Cox said. “This used to be an invisible disability. I’d get tired before other people or need to rest, but it wasn’t visible, and it was something I tried to hide. I was afraid directors wouldn’t understand. And they didn’t. I have had a lot of experiences where I was given a hard time because of things I couldn’t do. But since I started identifying as a disabled actor, my experience in the rehearsal room has been completely different.”

Three days into rehearsal, it was already clear Cox would bring unique elements to her role. She and Grayson ­DeJesus, as the Gentleman Caller who upsets the family’s delicate balance, were leaning on each other as they rehearsed a brief dance with choreographer Maija García.

“My mobility aid doesn’t have musculature that can hold me up. So I felt a lifting that I haven’t felt in a long time. And then we played with jumps. I don’t jump anymore, but using someone else, I could. I become so emotional, and I got choked up,” Cox said. “I felt physically free and supported in a way I haven’t in a while, and that’s how Laura feels, physically and emotionally, in the play. Connecting your physical life with your inner life is so much what disability in theater can be about.”

Cox thinks it leads to misconceptions if an able-bodied actor plays Laura.

“In the disabled community, some people roll their eyes at this character,” she said. “It’s probably the interpretation [they saw] because able-bodied actors usually played Laura.

“Because she’s disabled in whatever fashion, she doesn’t have any wants or needs or any agency of her own. Just a victim. In my opinion, that’s probably why some people have that opinion of this character, but I don’t think that’s anywhere in the text. I see her as a real person who wants things deeply.”

Just like everyone.

“People with disabilities are complicated and nuanced and multifaceted in the way that every human being is,” Linton said. “Let’s paint them in that light.”

Haj sees that as a big step in making American theater more inclusive. Linton thinks progress is being made, even if events such as the recent Tony Awards — where “Oklahoma” actor Ali Stroker became the first person in a wheelchair to win a Tony but had to await her award backstage because the stage was inaccessible — show there is work to be done.

Cox believes audiences intuit the difference between an actor who has a disability and one who does not.

“There’s something else that is opening a gateway to acceptance that isn’t opened when they know that at the end of the day their favorite actor who has the ‘perfect’ body can leave [their mobility aid] on the stage,” Cox said. “You realize this is a real person. You’re seeing the real thing and learning about it and opening your heart to it at the same time. I think there’s a big difference.”