I would point out, as an aside, that Opera itself is basically "an open-source community of musical-play development" — i.e. performances where the source material is in the public domain such that anyone can put on a performance of them without paying royalties.
This is unlike "musicals", which are protected by copyright, and are thus only run by the musical's rights-holder's licensed troupe(s), in a particular place (usually Broadway), with a particular interpretation of the material (the rights-holder's); where the revenues are due to high ticket prices that can be charged often only due to the artificially-created scarcity of performances of said musical due to IP law. (I.e. for many musical, nobody is going because they're fans of the particular actors/director/etc; they just wanted to see a performance of musical X, akin to what you'd get from seeing opera X. But there's only one available performance of a given musical X. Musical producers have a monopoly on performances of their musical.)
Musicals make money, by design. Opera does not make money, by design. Instead, opera houses take donations, in much the same way that you might imagine a "local open-source software development collective" might take donations.
When the people of a municipality get together and decide that they consider their local opera house a "local cultural institution" worth supporting with their tax money (usually only to prop it up in bad donation years), this does certainly make the opera house into a "government-backed" project. But in this case, the "government" here is just the mob-action of the people of the city. It's the atheist version of a church congregation agreeing that their tithes should be partly directed to some local needy cause.