When I lived in the UK as a university student years ago, I went to a local Aldi. There was no stigma there, perhaps because of the student population. I liked it for the quirky items and Germanness.

In the US, it has varied over time and by location. I'd say 20 years ago it was seen as more low class in places I've lived (DC, KC, Chicago, Dallas). In recent years, it's picked up a bit of a trendiness vibe and newer/renovated Aldi's seem fairly nice. (It maybe always had a trendy vibe near US universities...that part I don't know.) I have ventured into Aldi a couple times since they began accepting credit cards - the clientele was not noticeably different from any other area grocery store except perhaps gourmet/boutique stores.

Trader Joe's has always been trendy to the point where some people get obnoxious or borderline culty about it. Aldi isn't like that (yet).