Producers of the touring musical “Fun Home” — which opens Tuesday at the Orpheum Theatre — did not cast Kate Shindle in the lead role for guaranteed publicity, but it sure hasn’t hurt that everyone wants to talk to a former Miss America who is now president of the stage actors’ union and touring the country playing a famous lesbian.

Including, of course, the newspaper in a Midwestern city chock full of theatermakers and theater enthusiasts.

“I’m actually really looking forward to playing Minneapolis,” Shindle said, speaking recently from Detroit, fifth stop on the “Fun Home” tour. “It’s got an educated theatergoing audience that will really be ideal for our show.”

She hastily added, “Minneapolis gets all the good buzz, but St. Paul is awesome, too.”

Shindle recalls working in the Twin Cities after her 1998 Miss America win, but can’t remember which show. It just wasn’t at the Guthrie. (“That would be a dream, to work at the Guthrie.”) Now she’s starring in the 2015 Tony Award winner for best new musical, adapted by Jeanine Tesori and Lisa Kron from the hit graphic memoir by Alison Bechdel. Shindle’s “Big Alison” mostly serves as a narrator, observing the challenges faced by young “Small Alison” and teenage “Medium Alison,” both of whom are struggling to grow up in a home led by their closeted gay father. He’s an undertaker.

The role is not one you’d typically associate with a beauty queen. Shindle, who is straight but has long advocated for LGBT issues, cut her long auburn hair into a buzz cut and recently posed with the much more butch Bechdel for the New York Times, a paper that rarely gives significant coverage to Broadway tours.

The road show began this fall in Cleveland, and from there went to Durham, N.C., where it sold out, helped in part by sentiment against the state’s law restricting bathroom use by transgender people.

Shindle spoke about how the tour is going, the pros and cons of being tall and what she’s learning from actors in “flyover country.” 

Q: This is your first major role since becoming president of Actors’ Equity, right?

A: It is. I took some time off to learn the ropes, but at a certain point, I realized I had to start auditioning for things and make a living. Around that time I saw “Fun Home” on Broadway, and I really responded to it. It wasn’t just the writing, it was the voice and the message of the show. It was emotionally challenging, and it just added up to something I wanted to do. 

Q: You’re 5 feet 11. You told the New York Times that this was a role where your height — and potentially being paired with a shorter male partner — wouldn’t be an issue.

A: If I had a nickel for every day of my life I wished I was 5-5, I would have a nickel for every day of my life. But you have to take the good with the bad.

A lot of roles in the musical theater canon are boy-meets-girl type roles. Instead, I’ve been drawn toward roles where women are learning to navigate the world on their own. Shows like “Gypsy.” I loved doing “Gypsy.”

Q: You’re just wearing tennis shoes in “Fun Home,” right? You’re not towering over anyone in heels.

A: I’m wearing Converse. I’m on stage the whole time, but I don’t really have a scene partner, I’m the connective tissue. 

Q: In your off hours, are you meeting with Equity members?

A: I am. I expect to be doing that in Minneapolis. It’s a big priority of mine. There are members across the country who want to feel more connected to the union. 

Q: What concerns are you hearing?

A: A lot of lifestyle things. Four-week rehearsals versus eight-week rehearsals — sometimes shorter rehearsals over longer periods are easier for local actors. Housing, if you are working at a regional theater. In Florida, actors were being encouraged to print their own scripts. It’s not life or death, but if you are printing out a couple of hundred pages, you are running through printer ribbons. These aren’t things I would hear about on the 17th floor of the Equity building in Times Square, but they are things that come out over coffee. 

Q: How is “Fun Home” being received on the road compared with New York?

A: Overwhelmingly pretty positive. We had our first million-dollar week in Durham. To me, that says a lot of things. One, it says that there’s always an appetite for good theater, even if it’s a lesser-known title, and two, that no matter where you go, there are progressive thinkers everywhere. I so despise the term “flyover state.” It’s so dismissive.

Q: Steven Schwartz (“Wicked,” “Godspell”) isn’t even allowing his musicals to be performed in North Carolina.

A: There’s a time and place for voting with your wallet, and there’s a time and place for going on TV and saying, “I support the guy that’s challenging the governor.” 

Q: Are you getting lots of support from the LGBT community out on tour?

A: Yes, the community is coming, but the biggest question for me in interviews is how much to talk about LGBT themes. They are very important to the story, but I don’t want people to see that acronym and think, “This story is not for me.” This is a story about a family that looks perfect on the outside, and is not-so-perfect on the inside. 

Q: You’re coming to the Orpheum with “Fun Home” right after “The Curious Incident of the Dog in the Night-Time” played there. Neither show seems ideal for the holiday season.

A: What’s better than the holiday season if you are trying to relate to a family that is not as it appears and has all sorts of internal drama? Good theater is good theater.