I speak for the 18th century, which is admittedly a bit earlier than what you are talking about, however, from what I understand, opera-going life was broadly comparable.

The best way I can describe going to an opera is a bit like going to like a music festival today. It really is a venue for music, and plenty of people who go to them really are there for the music, but there are a ton of social reason to want to go as well. You can talk during shows, no one is going to give you dirty looks if you do, but there are also parts of the experience where everyone really is spellbound by the musical events they are hearing. Basically, there are fewer constraints on what you are allowed to do while the music is happening, but that doesn't mean no one is listening.

There's a really fascinating book that's the collected diaries of one Susan Burney, daughter of the eminent 18th century music historian Charles Burney. Reading just one of her diary entries can give you huge insights into what it was like to go to an opera in the 1780s. My personal favorite is the entry for March 8th, 1780, where she goes to see an opera called Olimpiade. Actually, she does three things: she goes to the rehearsal, then she goes to the opera itself, then she goes with her family to have an intimate meeting with one of the singers.

Here are sample of some of her experiences:

My Mother, Fanny, & I went [to the rehearsal]. & got into one of the stage Boxes -- As soon as [the singer] Pacchierotti arrived, I saw him approach to speak to some Company in the next Box - Whilst he was there, he perceived us, & bowed - of course enquiry was made of who his salutation was to, & in an instant Lady Clarges leant out of her box, & with her usual goodhumour ask'd me how I did... After this, during the Rehearsal & after it, we had a good deal of Musical Conversation, which was very pleasant to me, as I really love Lady Clarges, & she is to me always everything I can wish - Pacchierotti came to speak to us 2 or 3 times.

...

I was delighted with the Rehearsal, as the Olimpiade as now got up is a sweet pretty Pasticcio [an opera that is a medley of a bunch of arias from a bunch of different operas piled together] - though the Drama is so divine that it grieves one to have it so curtailed & mauled as it is...

Pacchierotti sung Superbo di me Stesso like an Angel - & the Duet, tho' he & [the singer] Mad. Le Brun were taken during it with some joke, & made it rather Comic than otherwise - instead of Cessa mio ben di piangere, Pacchierotti the second time said di ridere, which made them worse than ever.

Now onto the performance the next day:

In the evening [I] went with Fanny & Charlotte to the O: House. We arrived just as the overture began - Our Box was next to the Duke of Dorset's - & a more charming, comfortable one - I would not have changed it for any in the House - Lady Hales was on the Stage of our side - Mrs Castle & the Ogles &c in an upper stage Box - [She continues to list 30 other names] In short we had the satisfaction of seeing faces we know everywhere, & indeed a most brilliant House... I saw not [the composer] Sacchini - yet doubtless he was there, as Pacchierotti was to sing his Se cerca & not the same as last year's.

And now my favorite part of the whole journal:

In [Pacchierotti's] great Scene, Misero! Che Veggo &c [a scene culminating in the great aria Se cerca, se dice between the Drama - the Composition, & his performance I was - absolutely melted - I cried as I did at the first Serious Opera I heard, when Guadagni performed Orfeo - I never heard any thing more touching, nor shall ever recollect it without Emotion - Ah no, Si gran duolo non darla per me yet resounds in my ears - yet I heard his Sweet Voice, & such Music it is! - Oh! With how much feeling it is Set!! -

It was felt by the Audience wonderfully... No - Not wonderfully since it was felt only as it ought to be - Such a Murmur spread, especially from that corner of the Pitt where My Father sat, of whispered bravos as I scarce ever heard - & the moment, nay even before the song was quite done there was a burst of vehement applause, which affected me in a new way - indeed I felt sensations very exquisitely delightful - & I could write forever about this Scene -

Talk about an experience! But there are also remarks about the social aspects of the evening:

In the middle of the 3rd Act, while he was standing at one of the side scenes, [Pacchierotti] saw, & with a sweet smile bowed to us - which salutation we with more than our wonted affability returned - after this he had no rest, as every body was curtsying to him, even when he was on the stage, which I saw embarrassed even whilst it flattered him.

So I think there's a lot here to take in. First of all, we can see that it is not quite the solemn ritual that we expect from modern opera. It really is at least partially about seeing your friends. And the performers themselves even get in on the action: at the rehearsal, they may joke around and laugh during the middle of a piece, and even during the actual performance, they will break the fourth wall and acknowledge their friends in the audience.

But there are moments of true musical rapture as well. Susan's account of hearing "Se cerca, se dice" is just wonderful. And note how important the rest of the audience is to it: she's affected not only by the music, but by how overcome the whole audience seems to be. I'd actually say the social aspects of the event enhance this effect: these are not just faceless bodies sitting silent next to you like in modern opera houses, these are your friends, neighbors, acquaintences, cousins, and other people that you know intimately. To see a room full of familiar faces react viscerally to what's going on onstage could very well enhance your own reaction.

There are many such accounts of musical experiences throughout the eighteenth century. A lot of them are collected and analyzed in the first chapter of Martha Feldman's fantastic book Opera and Sovereignty. But while all of them paint a far more relaxed and socially-based opera-going atmosphere than we are used to from today, it is also far more complicated than "people didn't care about the music" the way some present-day commentators like to characterize it. Each concert report tells us of moments where the audience becomes absolutely spellbound by some (or several) incredible musical events on the stage. But the thing is, the audience's attentions were earned, not ensured by the structure of the event the way it is in our modern concert and theatre-going experience. If you wanted audiences to shut up and pay attention, you better work your creative (as a composer) and performative (as a singer) ass off to make it happen!