BUDAPEST — The grand, gilded Hungarian State Opera House here is where Brahms once heard Mahler conduct Mozart. It’s where Bartok’s still-shocking “Bluebeard’s Castle” had its premiere a century ago. It’s where the artist Matthew Barney shot part of his “Cremaster” cycle, and Jennifer Lawrence filmed scenes for her violent thriller “Red Sparrow,” in which she played a ballerina-turned-spy.

These days, the house is also emerging as a flash point in Hungary’s culture wars.

The opera company is in the midst of one of its biggest expansions ever, thanks to the investment of hundreds of millions of dollars by the increasingly autocratic right-wing government of Prime Minister Viktor Orban, who is building what he calls an “illiberal democracy” and has described Hungary’s theaters, opera houses and concert halls as “temples of national culture.” The money is paying for the first major overhaul of the State Opera since the Cold War, as well as a construction spree that will leave it with three theaters when work is completed next year.

But in the midst of its country’s rightward turn, the company has recently attracted controversy. It canceled some performances of the musical “Billy Elliot” after a conservative newspaper denounced the work as “gay propaganda” and staged “Porgy and Bess” with white singers, against the wishes of its creators’ estates.

This month, the State Opera and the Hungarian National Ballet are bringing 350 singers, dancers and musicians to New York to perform nearly two weeks of fully staged operas and ballets. The lineup includes “Bluebeard’s Castle,” Karl Goldmark’s rarely staged “The Queen of Sheba” and “Bank Ban,” an 1861 Ferenc Erkel work considered the national opera of Hungary, as well as ballets including “Swan Lake” and “Don Quixote.” The tour will run from Oct. 30 through Nov. 11 at the David H. Koch Theater at Lincoln Center.