I actually do wear a hearing aid, but people tell me that they don't notice. I also keep my hair a bit on the long side, so it's not usually visible. it's also very small.
I haven't really run into anyone who immediately ended a date, but I suspect that I've been declined for dates because of it. I have also gone on strings of dates with women where they eventually either just fizzled out and stopped accepting new dates, or they pulled the "let's just be friends" card. I would be foolish to attribute this all to my hearing loss (I can certainly be a difficult person at times), but part of me always wonders.
To answer your second question, I think there is still a small stigma attached to it. Glasses are ubiquitous in today's society. Hearing aids, not so much. That said, the bluetooth revolution in the last five years has gone a long, long, long way toward making it more acceptable (or at least normal) to see something sticking out of someone's ear. Little kids will sometimes come up and ask me what's in my ear, but adults never do.
That said, my hearing aid is amazing. It has Bluetooth capabilities. I can listen to music without having to wear headphones. I can stream a phone call directly to my hearing aid, without the awkwardness of trying to hold a phone speaker up to my hearing aid microphone. It has volume control, "restaurant mode" for loud situations, and even "music mode" that doesn't filter out background noise at all. It's pretty fantastic, and I think over time, it will only get better.
The biggest hassle I have right now with hearing aids is battery life. I've developed a sixth sense about it, where I'll just randomly think, "Huh. When's the last time I changed the battery?" and then an hour or two later it will die. Still, sometimes I'm caught unaware. One time I was at a job interview, and it died on me. I had to excuse myself and go get a fresh pack of batteries from a Walgreens across the street. They still passed me on to the next round of interviews. (I didn't get the job, though).
If I had a few million dollars to do a hardware startup, I would try and develop a hearing aid that runs off body heat or some other mechanism. The main reason hearing aids are so big is because the case has to hold the battery -- the battery is by far the biggest component. If we could get rid of it, it could just be a band-aid like strip on the back of the ear and practically invisible.
Sorry, I digress. Going back to your earlier questions, I should be clear that the visibility of the hearing aid is probably not a problem. The actual hearing loss is probably the biggest turn off. Hearing aids aren't like glasses, where you can technically get back to 20/20 vision with minor help. You never really get back to 100% hearing with a hearing aid. There's always something off. And even my friends sometimes get tired of me saying "What?" all the time.
I hope that was helpful. Feel free to email me if you have any further questions. I'm happy to answer. I believe my email is in my profile.