Who cares what they wear and doesn’t matter whether a wedding band or not. I think anyone professional or not should wear what they like and not care what the viewers think.
They should ignore their audience?
I think classical pianists should be more free about the way they dress on stage overall. If they're comfortable wearing big rings, then so be it.
I firmly believe that the dress code for classical musicians, especially males, has to lighten up. Music and art are not formal. They have never been that. Yet people go on the stage almost always either in a suit in boring colors, or a black/white t-shirt. Why? And what bad does a big ring or two do? or some color?
As much as I don't like the music making of Liberace, Lang Lang, or that organ player who's name i've forgotten (he was dubbed the "bad boy of the organ" or something), I do admire their courage. Yes, their outfits may be extravagant and sometimes even exaggerated and gaudy, but they're performers, not office workers. (I just remembered that Pogorelich sometimes also made bold style choices on the stage, and Goulda as well. Both far greater musicians than the afromentioned three.)
So, yes - I think that pianists absolutely can wear those rings if they want to.
The audience would not mind. The audience would be intrigued.