Part of its reputation for elitism could be that many of opera's greatest hits are in  Italian, French and German. Among native English speakers who aren't studious and who have only a high school education, it might seem that opera is only accessible to those with a higher education of a certain type.

That's all I have to offer.  I don't speak Italian, French or German, but I can appreciate the beauty of a lot of operatic music.  Of course, I played classical music in grade school, junior high school and high school.  That helps me appreciate the musical side of the operatic repertoire.

People who don't appreciate classical music sung in German, Italian or French might think that it is a musical form that only an elite could appreciate.

Associations, in general, have more to do with the audience than with the event itself.

Joseph, good point about operas being in a foreign language. I would add that beyond a foreign language there is an out-of-the-world aspect, the strange singing often accentuated in certain performances, the decor, which more so than theater give a separated from the world aspect, which is then easily associated with elitism. (Similarly to the high-couture fashion shows which obviously have a different feeling than the pret-a-porter:

)

Not that I want to compare the two.

You might also be interested, Tim, in the following discussion on elitism.