For context, I'm Hard of Hearing and recently went to a Broadway show. The theater gave me a set of headphones so I could listen to the singers at a much higher volume and actually understand the lyrics and generally enjoy the show. It made me wonder about life for those with hearing difficulties before modern technology, especially when art appreciation was (as I unertand it) basically a cultural requirement for nobility. What would my life have been like in such a time?
Great question! Thanks to those who pointed me to it. I'm going to answer from a hearing/social perspective, rather than an opera perspective, since that isn't my field.
In 1875, you're going to be less than 25 years away from the invention of the first hearing aid, the Akouphone, by American Miller Reese Hutchison. His technology derived from telephone technology, which was being developed while you're at the opera - but it isn't helping you there yet. (Side note: My favorite piece on Hutchison has got to be this article from a phrenology journal. Apparently his head measurements made him a good inventor...)
But since you haven't got an electric hearing aid yet, you're probably using a collapsible ear trumpet. This isn't going to make the opera enjoyable, exactly, as ear trumpets don't work that way. The smaller the device, the worse the sound quality - but letting your hearing loss be known was very undesirable, so you generally had small, collapsible devices around this time. (They get even smaller as the years go by, of course - see Dr. Jaipreet Virdi's excellent Hearing Happiness for a full examination of how and why hearing devices got turned into earrings, hairpins, etc. during the first part of the 20th century.)
So you've probably got an ear trumpet you can bring with you, but it's not very good - are you likely to follow what is going on? You can definitely chat with someone to find out what it's about, which will help. You might bring someone along to jot down notes for you as it's happening, as this was also common at the time (see Treitschke's use of notetakers in meetings).
By the way, before the advent of deaf education in the 18th and 19th centuries in Europe, most deaf people were barely educated and frequently isolated. Nobility might have gotten tutors, or they might not - Kaiser Wilhelm II was disabled and the family was incredibly embarrassed by it; Prince John was sent away out of the public eye because of his epilepsy. So maybe you had an education, or maybe you didn't (in Germany, the first school for the deaf didn't open until 1873) - and that means you might have been expected to participate in art appreciation, or maybe not. Your degree of deafness, and how old you were when it began, are big factors for whether or not you even have a chance to try to use that little ear trumpet in the first place...
If anyone is familiar with the publication of opera librettos, please share in a follow-up comment. I don't know if they were commonly published - it looks like Wagner's were collected for publication in the 1930s? - and that would make a big difference for deaf folks at the time. If the libretto were available, reading it would help them have conversations about it - whether or not they had actually seen it.