As much as I'd like to tell some people to shut up about the Dixie cup I've served their wine in, apparently the glass type does make a difference...
https://www.scientificamerican.com/a...affect-flavor/
I'd add that for me, shape is second to composition. Waterford crystal red wine glasses make the most beautiful ring when you toast. If there's more than just me rattling glasses around, they are a must to serve with.
The decanting process probably matters even more though. I ordered a gruener veltliner in Toronto and the waiter shook it up like a martini for thirty seconds. I don't think it mattered what style of glass it was served in after that.