I think I know a bit how u feel.
I once fell madly in love with a man. Obsessively in love in fact. Thought he was god's gift. I met him while I worked in a bar in London and he was a regular, he'd often stay after closing hours so I got to know him quite well.
We definitely got to know each other well enough before jumping into bed then moving in together. Apart from one thing.
So, he was in a one-hit-wonder "cult following" type band. They still gigged, and played at low key music festivals. My point is he wasn't famous not in the slightest, but he sort of acted like or thought that he was.
He wore sunglasses. All the time, I mean ALL the time. At night. Inside. Inside the pub, inside shops. Eating in restaurants.
When he'd come into the venue I worked, he'd wear his shades and I'd think it was quirky, but honestly thought he was wearing them because he was at this bar, and he took them off elsewhere. I fell in love with him knowing he wore shades like "a bit too much" but when we got more serious I realized it was obsessive and found it really embarrassing.
He'd wear them at the cinema for goodness sake!
I'm not a shallow person, really, but I ended up feeling so embarrassed by his stubborn and relentless shade wearing, (despite dropping hints and suggestions as you can imagine) our relationship was completely unsustainable, which was a great shame because we were great together other than that. If I'd just "gotten over it/used to it" it'd worked probably, but I couldn't ignore my feelings and if anything the more I tried to fight feeling embarrassed/self conscious when out with him, the worse it got.
So my point is, I think your feelings of embarrassment are a sign you are fundamentally incompatible in some way, but you can probably work through it if it's worth it.
It might be you who needs to change though.